This thesis investigates novel directions for harnessing the potential of quantum computers in future applications. It is structured into three sections.
\r\n\r\nQuantum Simulation.
\r\nWe address two key questions: what systems exhibit quantum advantage in predicting ground state properties, and how can we reduce the cost of quantum simulations? For the former, we find that strongly interacting fermionic systems have promising characteristics for quantum advantage. For the latter, we develop an improved method for compiling block encodings using sum-of-squares optimization.
Learning with Entangled Measurements.
\r\nWe explore the benefits of leveraging entangled measurements on quantum states stored in quantum memory. These learning algorithms can be applied to the readout stage of quantum simulations, or to learn from quantum data from nature.
Topological Data Analysis.
\r\n\r\nUsing complexity-theoretic insights, we demonstrate that certain problems in topological data analysis possess a quantum mechanical structure, suggesting opportunities for quantum algorithms in this area.
One of the primary motivations for building quantum computers is to simulate quantum many-body systems. While significant progress has been made in simulating quantum dynamics, much less is known about simulating ground states and Gibbs states, an essential task for understanding the static properties of quantum many-body systems. From a computer science perspective, problems on ground states and Gibbs states are quantum analogues of the Boolean satisfiability problem (SAT) and classical Gibbs sampling, which have wide applications in optimization, machine learning, and computational complexity.
\r\n\r\nThis thesis leverages tools from computer science to explore the potential quantum advantage in simulating ground states and Gibbs states, through two complementary approaches: designing new quantum algorithms and evaluating the extent to which classical algorithms remain effective. In particular, \r\n
Controlled quantum systems have the potential to make major advancements in tasks ranging from computing to metrology. In recent years, quantum devices have experienced tremendous progress, reaching meaningful, intermediate-scale sizes and demonstrating advantage over their classical counterparts. Still, sensing, learning, verifying, and hopefully mitigating errors in these systems is an outstanding and ubiquitous challenge facing all modern quantum platforms.
\r\n\r\nHere we review and expound upon one such platform: arrays of Rydberg atoms trapped in optical tweezers. We demonstrate several key advancements, including the first experimental realization of erasure conversion to prepare two-qubit Bell states with a fidelity in excess of 0.999, and to cool atoms to their motional ground state. We further showcase the tools of universal quantum processing via arbitrary single-qubit gates, fixed two-qubit gates, and mid-circuit measurement, and discuss applications of these techniques for metrology and computing.
\r\n\r\nThen, we turn to the many-body regime, generating highly entangled states with up to 60 atoms through analog quench dynamics. We reveal the emergence of random behavior from unitary quantum evolution, and uncover a universal form of quantum ergodicity linking quantum and statistical mechanics. We exploit these discoveries to verify the global many-body fidelity and then realize practical applications like parameter estimation and noise learning. Finally, we compare against both state-of-the-art quantum and classical processors: we introduce a new proxy for the experimental mixed state entanglement which is comparable amongst all quantum platforms, and that reflects the classical complexity of quantum simulation.
", "doi": "10.7907/t7jr-mf97", "publication_date": "2024", "thesis_type": "phd", "thesis_year": "2024" }, { "id": "thesis:16388", "collection": "thesis", "collection_id": "16388", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05172024-212658426", "primary_object_url": { "basename": "Gu_Shouzhen_2024.pdf", "content": "final", "filesize": 3702205, "license": "other", "mime_type": "application/pdf", "url": "/16388/1/Gu_Shouzhen_2024.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Quantum Error Correction Using Low-Density Parity-Check Codes and Erasure Qubits", "author": [ { "family_name": "Gu", "given_name": "Shouzhen", "orcid": "0000-0003-2560-4209", "clpid": "Gu-Shouzhen" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "Quantum error correction is a method to reduce the effective error rate on quantum computers so that they can be used to carry out useful computation. In this thesis, we study two main problems: decoding quantum low-density parity-check codes and using erasure qubits to implement error correction protocols.
\r\n\r\nIn the first part of this thesis, we focus on quantum low-density parity-check codes, which are a promising approach to reducing the spacetime overhead associated with error correction. We show that certain families of codes with constant rate and linear distance can be decoded efficiently. In particular, we propose a linear-time algorithm that will correct any error affecting at most a constant fraction of the qubits.
\r\n\r\nWe also analyze the setting where the measurement outcomes given to the decoder can be corrupted. In this more realistic scenario, the decoder is shown to have the single-shot property. Using one round of noisy syndrome data, it can output a correction that is close to the data error as long as at most a constant fraction of the data qubits and syndrome bits are flipped. As a consequence, the decoder can operate under a stochastic noise model where errors occur with sufficiently small but constant probability.
\r\n\r\nIn the second part of the thesis, we analyze quantum error-correcting codes implemented using erasure qubits. The idea behind erasure qubits is to bias the noise into a form where likely locations of errors are known, for example, by converting the dominant noise source into detectable leakage from the computational subspace. We provide a formalism for simulating and decoding stabilizer circuits with erasures, erasure checks, and resets. Using this formalism, we study the performance of Floquet codes and show that the benefits of knowing error locations outweigh the cost of extra noise due to erasure checks.
\r\n\r\nLastly, we optimize erasure check schedules in the context of the surface code. By performing simulations with one, two, or four erasure checks per syndrome extraction round, we find different error parameter regimes where it is optimal to use each schedule. Additionally, we provide a simplified way of decoding erasure circuits suitable for circuits with infrequent erasure checks.
", "doi": "10.7907/5pj8-wv34", "publication_date": "2024", "thesis_type": "phd", "thesis_year": "2024" }, { "id": "thesis:16064", "collection": "thesis", "collection_id": "16064", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06022023-202038500", "primary_object_url": { "basename": "Caltech_Thesis (8).pdf", "content": "final", "filesize": 1383310, "license": "other", "mime_type": "application/pdf", "url": "/16064/1/Caltech_Thesis (8).pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Revocable Cryptography in a Quantum World", "author": [ { "family_name": "Poremba", "given_name": "Alexander Mario", "orcid": "0000-0002-7330-1539", "clpid": "Poremba-Alexander-Mario" } ], "thesis_advisor": [ { "family_name": "Vidick", "given_name": "Thomas G.", "orcid": "0000-0002-6405-365X", "clpid": "Vidick-T" } ], "thesis_committee": [ { "family_name": "Mahadev", "given_name": "Urmila", "clpid": "Mahadev-Urmila" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Umans", "given_name": "Christopher M.", "orcid": "0000-0002-6390-9401", "clpid": "Umans-C-M" }, { "family_name": "Vidick", "given_name": "Thomas G.", "orcid": "0000-0002-6405-365X", "clpid": "Vidick-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Quantum cryptography leverages unique features of quantum mechanics in order to construct cryptographic primitives which are oftentimes impossible for digital computers. Cryptographic applications of quantum computers therefore have the potential for useful quantum advantage---entirely without computational speed-ups. Can we use the power of quantum states to address fundamental limitations in the world of classical cryptography, such as the intricate problem of ``revoking'' information from an untrusted party? This thesis undertakes a systematic study of how to delegate and revoke privileges in a world in which quantum computers become widely available. As part of a single framework we call revocable cryptography, we show how to revoke programs, encrypted data, and even cryptographic keys under standard assumptions.
\r\n\r\nIn the first part of this thesis, we focus on the following question: can we use the no-cloning principle of quantum mechanics and encode a program in such a way that it can be evaluated, yet it cannot be pirated? Naturally, we would also like to ensure that, once the program is ``returned,'' the recipient loses its ability to evaluate it. While this quantum notion of secure software leasing (SSL) was shown to be impossible for general programs by Ananth and La Placa (Eurocrypt 2021), their work left open the possibility that it is achievable for more primitive classes of programs. We construct an SSL scheme for a large class of evasive functions known as compute-and-compare programs---a more expressive generalization of point functions. Our scheme can be instantiated with any cryptographic hash function, and we prove its security in the quantum random oracle model. As a complementary result, we also construct a quantum copy-protection scheme for multi-bit point functions, which achieves a related but stronger notion of software protection previously introduced by Aaronson (CCC 2009).
\r\n\r\nIn the second part of this thesis, we ask: is it possible to provably delete information by leveraging the laws of quantum mechanics? We revisit a cryptographic notion called certified deletion, which was proposed by Broadbent and Islam (TCC 2020). While this remarkable notion allows a classical verifier to be convinced that quantum ciphertext has been deleted by an untrusted party, it offers no additional layer of functionality. We use Gaussian superpositions over lattices to construct the first fully homomorphic encryption scheme with certified deletion -- a protocol which allows an untrusted quantum server to compute on encrypted data and to also prove data deletion to a client. Our scheme has the desirable property that verification of a deletion certificate is public; meaning anyone can verify whether deletion has taken place. Assuming the quantum subexponential hardness of the learning with errors problem (Regev, STOC 2005), we can prove that our scheme achieves a particularly strong information-theoretic deletion guarantee; namely, once a valid deletion certificate is presented, the plaintext remains hidden even if the adversary is subsequently allowed to run in unbounded time.
\r\n\r\nIn the final part of this thesis, we ask: is it possible to revoke a crytographic key by using the power of quantum information? We give an affirmative answer to this question and design cryptosystems with key-revocation capabilities; specifically, we consider schemes with the guarantee that, once the secret key (represented as a quantum state) is successfully revoked from a user, they no longer have the ability to perform the same functionality as before. We define and construct several fundamental cryptographic primitives with key-revocation capabilities, namely pseudorandom functions, secret-key and public-key encryption, and even fully homomorphic encryption, assuming the subexponential hardness of the learning with errors problem. Central to all our constructions is our approach for making the Dual-Regev encryption scheme (Gentry, Peikert and Vaikuntanathan, STOC 2008) revocable.
", "doi": "10.7907/y62s-j417", "publication_date": "2023", "thesis_type": "phd", "thesis_year": "2023" }, { "id": "thesis:16112", "collection": "thesis", "collection_id": "16112", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06122023-221753249", "type": "thesis", "title": "Lorentz Symmetry and Non-Unitary Quantum Field Theories", "author": [ { "family_name": "Wang", "given_name": "Tian", "orcid": "0009-0001-4677-447X", "clpid": "Wang-Tian" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Kapustin", "given_name": "Anton N.", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" }, { "family_name": "Albert", "given_name": "Victor", "orcid": "0000-0002-0335-9508", "clpid": "Albert-Victor" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "We know quantum field theory is unitary. However, since the early 1980s, there have been numerous attempts to construct quantum field theories where time evolution is non-unitary. Some of these endeavors aimed to address the issue of black hole information loss, as non-unitary evolution does not necessarily require information preservation. Some wanted to use it as a modification of quantum mechanics to allow objective collapse. Some wanted to construct classical-quantum gravity which could serve as an alternative to quantum gravity.
\r\n\r\nI embarked on a similar path, attempting to construct a Lorentz covariant non-unitary quantum field theory. At a certain point, I believed we were making significant progress. However, I gradually realized that our construction faced serious problems. We took a lot of assumptions and results from unitary quantum field theory for granted, and used them without justification. After struggling with it for a long time, I decide to make a complete reversal and prove that non-unitary quantum field theories fundamentally conflict with Lorentz covariance.
\r\n\r\nThere are three approaches to constructing a Lorentz covariant non-unitary QFT. The first approach involves constructing a theory based on unitary quantum field theory, where a system is coupled to an environment. If we only consider the system and trace out the environment, the resulting equation of motion appears non-unitary. In this case, unitarity emerges as an emergent property. The second approach is to propose a theory from scratch where the time evolution is fundamentally non-unitary, described by the Lindblad master equation. Both in the emergent and fundamentally non-unitary theories, the dynamics are intended to be Lorentz covariant. The third approach employs the Schwinger-Keldysh formalism to construct a path integral, and examines the symmetry of the Keldysh action within the path integral. It is assumed that, similar to quantum field theory, the non-unitary theory will possess the same symmetry as the Keldysh action.
\r\n\r\nRegrettably, none of these three classes of theories prove successful. This thesis thoroughly analyzes the issues associated with these three constructions. The most significant problems include:
\r\n\r\n1, The fundamental assumption that the quantum fields (and their excitations) form a unitary representation of the Lorentz group is invalid, and they cannot form a non-unitary representation either.
\r\n\r\n2, The system Hamiltonian in the Lindblad equation is ill-defined and does not transform as the first component of a Lorentz four-vector.
\r\n\r\n3, Even if we overlook the aforementioned inconsistencies, the dynamics fail to produce expected results when applied to phenomena such as particle decay, as they exhibit a preferred reference frame.
\r\n\r\n4, The symmetry of the Keldysh action does not guarantee the corresponding symmetry in the dynamics. Invariant Keldysh actions can correspond to non-covariant equations of motion.
\r\n\r\nIn conclusion, the Lorentz symmetry is incompatible with non-unitary quantum field theories.
", "doi": "10.7907/h2d6-8387", "publication_date": "2023", "thesis_type": "phd", "thesis_year": "2023" }, { "id": "thesis:14645", "collection": "thesis", "collection_id": "14645", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05272022-220331463", "primary_object_url": { "basename": "Wilbur_Shirley_Thesis.pdf", "content": "final", "filesize": 26187118, "license": "other", "mime_type": "application/pdf", "url": "/14645/1/Wilbur_Shirley_Thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Structure of Entanglement in Fracton Phases of Matter", "author": [ { "family_name": "Shirley", "given_name": "Wilbur Eric", "orcid": "0000-0002-4970-1460", "clpid": "Shirley-Wilbur-Eric" } ], "thesis_advisor": [ { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis discusses recent contributions to the theory of gapped fracton phases of matter, utilizing exactly solvable Hamiltonian models as the primary tool of study. A large component of the work revolves around the notion of a foliation structure, which is a defining feature of the long-range entanglement in certain gapped fracton states. We introduce this concept, identify its presence in a handful of prominent fracton models, and explore its consequences in terms of entanglement entropy and fractional excitations. A second major theme of the thesis is the characterization of gapped fracton states via emergent gauge theories based on discrete subsystem symmetries. We introduce a variety of novel fractonic gauge theories including twisted and fermionic variants, identify their emergence in a bevy of well-known models, and classify them with the use of novel topological invariants. We also establish a link between subsystem symmetry and entanglement renormalization group flow in fractal spin liquids.
", "doi": "10.7907/7b2c-2e06", "publication_date": "2022", "thesis_type": "phd", "thesis_year": "2022" }, { "id": "thesis:14495", "collection": "thesis", "collection_id": "14495", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:02122022-205429202", "primary_object_url": { "basename": "PhDthesis_EunjongKim_rev1.pdf", "content": "final", "filesize": 35817420, "license": "other", "mime_type": "application/pdf", "url": "/14495/1/PhDthesis_EunjongKim_rev1.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Waveguide Quantum Electrodynamics in Superconducting Circuits", "author": [ { "family_name": "Kim", "given_name": "Eun Jong", "orcid": "0000-0003-4879-8819", "clpid": "Kim-Eun-Jong" } ], "thesis_advisor": [ { "family_name": "Painter", "given_name": "Oskar J.", "orcid": "0000-0002-1581-9209", "clpid": "Painter-O" } ], "thesis_committee": [ { "family_name": "Faraon", "given_name": "Andrei", "orcid": "0000-0002-8141-391X", "clpid": "Faraon-A" }, { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" }, { "family_name": "Painter", "given_name": "Oskar J.", "orcid": "0000-0002-1581-9209", "clpid": "Painter-O" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "Kavli Nanoscience Institute" }, { "literal": "div_eng" } ], "abstract": "Achieving an efficient interface of light and matter has been a principal goal in the field of quantum optics. A burgeoning paradigm in the study of light-matter interface is waveguide quantum electrodynamics (QED), where quantum emitters are coupled to a common one-dimensional waveguide channel. In this scenario, cooperative effects among quantum emitters emerge as a result of real and virtual exchange of photons, giving rise to new ways of controlling matter.
\r\n\r\nSuperconducting quantum circuits offer an exciting platform to study quantum optics in the microwave domain with artificial quantum emitters interfaced to engineered photonic structures on chip. Beyond revisiting the experiments performed in atom-based platforms, superconducting circuits enable exploration of novel regimes in quantum optics that are otherwise prohibitively challenging to achieve. Moreover, the unprecedented level of control over individual quantum degrees of freedom and good scalability of the system provided by state-of-the-art circuit QED toolbox set a promising direction towards the study of quantum many-body phenomena.
\r\n\r\nIn this thesis, I discuss waveguide QED experiments performed in superconducting quantum circuits where transmon qubits are coupled to engineered microwave waveguides. Employing the high flexibility and controllability of superconducting quantum circuits, we realize and explore various schemes for generating waveguide-mediated interactions between superconducting qubits. We also demonstrate an intermediate-scale quantum processor based on a dispersive waveguide QED system involving ten superconducting qubits, exploring quantum many-body dynamics in a highly controllable fashion. The work described in the thesis marks an important step towards the construction of scalable architectures for quantum simulation of many-body models and realization of efficient coupling schemes for quantum computation.
", "doi": "10.7907/bscv-b073", "publication_date": "2022", "thesis_type": "phd", "thesis_year": "2022" }, { "id": "thesis:14618", "collection": "thesis", "collection_id": "14618", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05252022-172723896", "type": "thesis", "title": "Quantum Constructions on Hamiltonians, Codes, and Circuits", "author": [ { "family_name": "Bohdanowicz", "given_name": "Thomas Christopher", "clpid": "Bohdanowicz-Thomas-Christopher" } ], "thesis_advisor": [ { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" }, { "family_name": "Endres", "given_name": "Manuel A.", "orcid": "0000-0002-4461-224X", "clpid": "Endres-M" }, { "family_name": "Flammia", "given_name": "Steven T.", "orcid": "0000-0002-3975-0226", "clpid": "Flammia-Steven-T" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis covers three different and largely unrelated projects from my time as a Ph.D. student studying quantum information and computation.
\r\n\r\nIn the first chapter, we construct a Hamiltonian whose dynamics simulate the dynamics of every other Hamiltonian up to exponentially long times in the system size. The Hamiltonian is time independent, local, one dimensional, and translation invariant. As a consequence, we show (under plausible computational complexity assumptions) that the circuit complexity of the unitary dynamics under this Hamiltonian grows steadily with time up to an exponential value in system size. This result makes progress on a recent conjecture by Susskind, in the context of the AdS/CFT correspondence, that the time evolution of the thermofield double state of two conformal field theories with a holographic dual has circuit complexity increasing linearly in time, up to exponential time.
\r\n \r\nIn the second chapter, we study approximate quantum low-density parity-check (QLDPC) codes, which are approximate quantum error-correcting codes specified as the ground space of a frustration-free local Hamiltonian, whose terms do not necessarily commute. Such codes generalize stabilizer QLDPC codes, which are exact quantum error-correcting codes with sparse, low-weight stabilizer generators (i.e. each stabilizer generator acts on a few qubits, and each qubit participates in a few stabilizer generators). Our investigation is motivated by an important question in Hamiltonian complexity and quantum coding theory: do stabilizer QLDPC codes with constant rate, linear distance, and constant-weight stabilizers exist?
\r\n\r\nWe show that obtaining such optimal scaling of parameters (modulo polylogarithmic corrections) is possible if we go beyond stabilizer codes: we prove the existence of a family of [[N, k, d, \u03b5]] approximate QLDPC codes that encode k = \u03a9̃(N) logical qubits into N physical qubits with distance d = \u03a9̃(N) and approximation infidelity \u03b5 = \u2134(1/polylog(N)). The code space is stabilized by a set of 10-local noncommuting projectors, with each physical qubit only participating in \u2134(polylogN) projectors. We prove the existence of an efficient encoding map and show that the spectral gap of the code Hamiltonian scales as \u03a9̃(N-3.09). We also show that arbitrary Pauli errors can be locally detected by circuits of polylogarithmic depth.
\r\n\r\nOur family of approximate QLDPC codes is based on applying a recent connection between circuit Hamiltonians and approximate quantum codes (Nirkhe, et al., ICALP 2018) to a result showing that random Clifford circuits of polylogarithmic depth yield asymptotically good quantum codes (Brown and Fawzi, ISIT 2013). Then, in order to obtain a code with sparse checks and strong detection of local errors, we use a spacetime circuit Hamiltonian construction in order to take advantage of the parallelism of the Brown-Fawzi circuits.
\r\n\r\nThe analysis of the spectral gap of the code Hamiltonian is the main technical contribution of this work. We show that for any depth D quantum circuit on n qubits there is an associated spacetime circuit-to-Hamiltonian construction with spectral gap \u03a9(n-3.09D-2log-6(n)). To lower bound this gap we use a Markov chain decomposition method to divide the state space of partially completed circuit configurations into overlapping subsets corresponding to uniform circuit segments of depth log n, which are based on bitonic sorting circuits. We use the combinatorial properties of these circuit configurations to show rapid mixing between the subsets, and within the subsets we develop a novel isomorphism between the local update Markov chain on bitonic circuit configurations and the edge-flip Markov chain on equal-area dyadic tilings, whose mixing time was recently shown to be polynomial (Cannon, Levin, and Stauffer, RANDOM 2017). Previous lower bounds on the spectral gap of spacetime circuit Hamiltonians have all been based on a connection to exactly solvable quantum spin chains and applied only to 1+1 dimensional nearest-neighbor quantum circuits with at least linear depth.
\r\n\r\nIn the third and final chapter, we study the problem of maximum-likelihood (ML) decoding of stabilizer codes under circuit level noise. As progress in the design of proposed fault-tolerant quantum computing architectures moves forward, it is becoming essential to achieve the highest noise suppression possible from the underlying quantum error correcting code. The decoder, which ultimately decides which correction to apply to an encoded state that has suffered an error, is an essential part of this design. So-called maximum likelihood decoders achieve optimal error suppression, but using such a decoder becomes intractable as the size of code grows, therefore sub-optimal decoders which achieve good performance and favorable implementation complexity are used instead. Circuit level noise presents a particular challenge for achieving good performance and practical complexity. We present the construction of a subsystem code called the Circuit History Code which provides an algebraic structure for understanding and classifying circuit level errors. We use this structure to formulate maximum likelihood decoding under circuit level noise as a tensor network contraction. This in turn allows the implementation of approximate maximum likelihood decoders which we expect could provide near optimal decoding performance with considerably lower complexity. Using tensor network ML decoders can be useful for benchmarking the performance of efficient decoders being designed for implementation in real experiments, as well as providing options for implementing decoders for codes that would be difficult to decode with conventional methods.
", "doi": "10.7907/pxp0-aw46", "publication_date": "2022", "thesis_type": "phd", "thesis_year": "2022" }, { "id": "thesis:14411", "collection": "thesis", "collection_id": "14411", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10292021-071119947", "type": "thesis", "title": "Random Quantum Circuits and Their Simulation Complexity: an Analysis with Statistical Mechanics", "author": [ { "family_name": "Dalzell", "given_name": "Alexander Moos", "orcid": "0000-0002-3756-8500", "clpid": "Dalzell-Alexander-Moos" } ], "thesis_advisor": [ { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Painter", "given_name": "Oskar J.", "orcid": "0000-0002-1581-9209", "clpid": "Painter-O" }, { "family_name": "Vidick", "given_name": "Thomas G.", "orcid": "0000-0002-6405-365X", "clpid": "Vidick-T" }, { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Random circuit simulation, the task of replicating the output of a randomly chosen noiseless quantum computation, has been proposed as a path toward achieving quantum advantage: it is believed to be easy for quantum devices, but hard for classical ones. This thesis scrutinizes both sides of this belief. On the one hand, we investigate whether the task is classically hard\u2014we find that, in certain non-trivial cases, it can actually be easy, complicating a potential general proof of hardness. On the other hand, we investigate whether the task can be easily accomplished on realistic quantum devices, which are subject to substantial noise rates\u2014we find that, indeed, a version of the circuit simulation task can be salvaged even on a noisy quantum device performing the computation with low fidelity, as long as the noise meets certain conditions. Thus, this thesis emphasizes that, to construct a strong argument of quantum advantage via random circuit simulation on noisy quantum hardware, the core theoretical challenge remains proving lower bounds on the classical complexity of the task; doing so will require new ideas to circumvent the barriers presented by our work.
\r\n \r\nA key analytical technique we utilize for each of our results is the statistical mechanics method for random quantum circuits, which maps random quantum circuits made from local Haar-random gates to partition functions of classical statistical mechanical systems. This thesis demonstrates the utility of this method by applying it in several new ways. In some cases, we use it for heuristic reasoning about the behavior of random quantum circuits. In others, we go further and perform rigorous calculations of the resulting partition function, leading to precise technical conclusions about random quantum circuits, such as sharp bounds on the number of random gates needed to achieve the anti-concentration property.
", "doi": "10.7907/3ntn-n574", "publication_date": "2022", "thesis_type": "phd", "thesis_year": "2022" }, { "id": "thesis:14142", "collection": "thesis", "collection_id": "14142", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05112021-210031085", "type": "thesis", "title": "Does Richard Feynman Dream of Electric Sheep? Topics on Quantum Field Theory, Quantum Computing, and Computer Science", "author": [ { "family_name": "Liu", "given_name": "Junyu", "orcid": "0000-0003-1669-8039", "clpid": "Liu-Junyu" } ], "thesis_advisor": [ { "family_name": "Cheung", "given_name": "Clifford W.", "orcid": "0000-0002-9983-9425", "clpid": "Cheung-Clifford" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Simmons-Duffin", "given_name": "David", "orcid": "0000-0002-2937-9515", "clpid": "Simmons-Duffin-D" } ], "thesis_committee": [ { "family_name": "Patterson", "given_name": "Ryan B.", "orcid": "0000-0002-5787-9517", "clpid": "Patterson-R-B" }, { "family_name": "Cheung", "given_name": "Clifford W.", "orcid": "0000-0002-9983-9425", "clpid": "Cheung-Clifford" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Simmons-Duffin", "given_name": "David", "orcid": "0000-0002-2937-9515", "clpid": "Simmons-Duffin-D" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "In this thesis, we mainly discuss three topics in theoretical physics: a proof of the weak gravity conjecture, a basic statement in the string theory landscape using the black hole entropy, solving the critical O(3) model using the conformal bootstrap method involving semidefinite programming, and numerical simulation of the false vacuum decay using tensor network methods. Those topics cover different approaches to deep understanding of quantum field theories using concepts and methods of information theory, and computer science with classical and quantum computations.
", "doi": "10.7907/adtc-ss13", "publication_date": "2021", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:14152", "collection": "thesis", "collection_id": "14152", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05182021-042001387", "primary_object_url": { "basename": "tang_yuqing_thesis.pdf", "content": "final", "filesize": 20299777, "license": "other", "mime_type": "application/pdf", "url": "/14152/2/tang_yuqing_thesis.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Quantum Information at High and Low Energies", "author": [ { "family_name": "Tang", "given_name": "Yu Qing (Eugene)", "orcid": "0000-0003-4275-0398", "clpid": "Tang-Yu-Qing-Eugene" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "In this thesis, we take a look at how quantum information theory can be used to study physical systems at both high and low energies.
\r\n\r\nIn the first part of this thesis, we examine the structure of the low-energy subspaces of quantum many-body systems. We show that the existence of error-correcting properties in low-energy subspaces is a generic feature of quantum systems. Using the formalism of matrix product states, we construct explicit quantum error-detecting codes formed from the momentum eigenstates of a quantum many-body system.
\r\n\r\nWe also examine how topological order can persist past the ground state space into the low-energy subspace of excited states by studying the No Low-Energy Trivial States (NLTS) conjecture. We prove a version of the NLTS conjecture under the assumption of symmetry protection. Moreover, we show that our symmetric NLTS result has implications for the performance of quantum variational optimization algorithms by using it to prove a bound on the Quantum Approximate Optimization Algorithm (QAOA).
\r\n\r\nIn the second part of this thesis, we examine problems related to bulk reconstruction in holography and the black hole firewall paradox. Using the formalism of the tensor Radon transform, we devise and implement a numerical algorithm for reconstructing (perturbatively in AdS\u2083/CFT\u2082) the bulk metric tensor from a given boundary entropy profile.
\r\n\r\nWe finally examine the black hole firewall problem from the perspective of quantum error-correction and quantum computational complexity. We argue that the state of the Hawking radiation has the special property of being computationally pseudorandom, meaning that it cannot be distinguished from the maximally mixed state by any efficient quantum computation. We show that this implies that each black hole has a natural structure as a quantum error-correcting code.
", "doi": "10.7907/xc66-tc77", "publication_date": "2021", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:13624", "collection": "thesis", "collection_id": "13624", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01162020-013448014", "type": "thesis", "title": "Quantum Correlations, Certifying Quantum Devices, and the Quest for Infinite Entanglement", "author": [ { "family_name": "Coladangelo", "given_name": "Andrea Wei", "orcid": "0000-0002-6773-2711", "clpid": "Coladangelo-Andrea-Wei" } ], "thesis_advisor": [ { "family_name": "Vidick", "given_name": "Thomas G.", "orcid": "0000-0002-6405-365X", "clpid": "Vidick-T" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" }, { "family_name": "Vidick", "given_name": "Thomas G.", "orcid": "0000-0002-6405-365X", "clpid": "Vidick-T" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Quantum information has the potential to disrupt the present computational landscape. Much of this potential rests on the existence of efficient quantum algorithms for classically intractable problems and of quantum cryptographic protocols for tasks that are provably impossible to realize classically. At the heart of many quantum advantages is one of the most counterintuitive features of quantum mechanics, known as entanglement. The central motivating question of this thesis is the following: if quantum devices will perform tasks that are beyond the reach of classical devices, can we hope to certify that they are performing these tasks correctly? Bell's theorem, a landmark result in physics, provides a partial answer to this question: it asserts that measurements on spatially isolated, but entangled, particles can result in outcomes that are correlated in a way that cannot be explained by any local hidden variable theory (such as Newtonian physics). A direct operational consequence of this theorem is that one can devise a statistical test to certify the presence of entanglement (and hence of genuine quantumness). Remarkably, nature allows us to take this certification one step further: in some cases, the correlation of measurement outcomes is sufficient to single out a unique quantum setup compatible with this correlation. This phenomenon is often referred to as self-testing, and is the central topic of this thesis.
\r\n\r\nIn the first part of this thesis, we review the basic terminology and results in the theory of self-testing. We then explore a concrete application to the problem of verifiably delegating a quantum computation. Our main technical contribution is a test that robustly certifies products of single-qubit Clifford measurements on many EPR pairs. We employ this test to obtain a protocol which allows a classical user to verifiably delegate her quantum computation to two spatially isolated quantum servers. The overall complexity of our protocol is near-optimal, requiring resources that scale almost linearly in the size of the circuit being delegated.
\r\n\r\nIn the second part of this thesis, the driving question is the following: what is the class of quantum states and measurements that can be certified through self-testing? Does self-testing only apply to a few special cases, like EPR pairs or copies of EPR pairs, or are these instances of a more general phenomenon? One of the main results of this thesis is that we settle this question for the case of bipartite states. We show the existence of a self-testing correlation for any pure bipartite entangled state of any finite local dimension. We then move on to explore the multipartite case, and we show that a significantly larger class of states can be self-tested than was previously known. This includes all multipartite partially entangled GHZ states, and more generally all multipartite qudit states which admit a Schmidt decomposition.
\r\n\r\nIn the final part of this thesis, we explore connections of the theory of self-testing to basic questions about entanglement and quantum correlation sets. In particular, we set out to understand the expressive power of infinite-dimensional quantum systems. We consider two questions: can spatially isolated quantum systems of infinite dimension produce correlations that are unattainable by finite-dimensional systems? Does there exist a correlation that cannot be attained exactly by spatially isolated quantum systems (not even infinite-dimensional ones), but can be approximated arbitrarily well by a sequence of finite or infinite-dimensional systems? The first question was posed by Tsirelson in 1993, and its answer has been elusive. One of the main results of this thesis is a resolution of this question. The second question is better known as the \"non-closure of the set of quantum correlations\", and was answered affirmatively in a breakthrough of Slofstra. We give a new elementary proof of this result which leverages one of our self-testing results and a phenomenon known as embezzlement.
\r\n", "doi": "10.7907/VQC0-ZK80", "publication_date": "2020", "thesis_type": "phd", "thesis_year": "2020" }, { "id": "thesis:13734", "collection": "thesis", "collection_id": "13734", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05292020-005036817", "primary_object_url": { "basename": "Singh_Ashmeet_2020.pdf", "content": "final", "filesize": 3661638, "license": "other", "mime_type": "application/pdf", "url": "/13734/1/Singh_Ashmeet_2020.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Quantum Mechanical Vistas on the Road to Quantum Gravity", "author": [ { "family_name": "Singh", "given_name": "Ashmeet", "orcid": "0000-0002-4404-1416", "clpid": "Singh-Ashmeet" } ], "thesis_advisor": [ { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" }, { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" }, { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" } ], "local_group": [ { "literal": "Walter Burke Institute for Theoretical Physics" }, { "literal": "div_pma" } ], "abstract": "In this thesis, we lay out the goal, and a broad outline, for a program that takes quantum mechanics in its minimal form to be the fundamental ontology of the universe. Everything else, including features like space-time, matter and gravity associated with classical reality, are emergent from these minimal quantum elements. We argue that the Hilbert space of quantum gravity is locally finite-dimensional, in sharp contrast to that of conventional field theory, which could have observable consequences for gravity. We also treat time and space on an equal footing in Hilbert space in a reparametrization invariant setting and show how symmetry transformations, both global and local, can be treated as unitary basis changes.
\r\n\r\nMotivated by the finite-dimensional context, we use Generalized Pauli Operators as finite-dimensional conjugate variables and define a purely Hilbert space notion of locality based on the spread induced by conjugate operators which we call \"Operator Collimation.\" We study deviations in the spectrum of physical theories, particularly the quantum harmonic oscillator, induced by finite-dimensional effects, and show that by including a black hole-based bound in a lattice field theory, the quantum contribution to the vacuum energy can be suppressed by multiple orders of magnitude.
\r\n\r\nWe then show how one can recover subsystem structure in Hilbert space which exhibits emergent quasi-classical dynamics. We explicitly connect classical features (such as pointer states of the system being relatively robust to entanglement production under environmental monitoring and the existence of approximately classical trajectories) with features of the Hamiltonian. We develop an in-principle algorithm based on extremization of an entropic quantity that can sift through different factorizations of Hilbert space to pick out the one with manifest classical dynamics. This discussion is then extended to include direct sum decompositions and their compatibility with Hamiltonian evolution.
\r\n\r\nFollowing this, we study quantum coarse-graining and state-reduction maps in a broad context. In addition to developing a first-principle quantum coarse-graining algorithm based on principle component analysis, we construct more general state-reduction maps specified by a restricted set of observables which do not span the full algebra (as could be the case of limited access in a laboratory or in various situations in quantum gravity). We also present a general, not inherently numeric, algorithm for finding irreducible representations of matrix algebras.
\r\n\r\nThroughout the thesis, we discuss implications of our work in the broader goal of understanding quantum gravity from minimal elements in quantum mechanics.
", "doi": "10.7907/m1vx-d174", "publication_date": "2020", "thesis_type": "phd", "thesis_year": "2020" }, { "id": "thesis:13729", "collection": "thesis", "collection_id": "13729", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05282020-140924661", "primary_object_url": { "basename": "Joe_Iverson_Thesis.pdf", "content": "final", "filesize": 3673146, "license": "other", "mime_type": "application/pdf", "url": "/13729/1/Joe_Iverson_Thesis.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Aspects of Fault-Tolerant Quantum Computation", "author": [ { "family_name": "Iverson", "given_name": "Joseph Kramer", "orcid": "0000-0003-4665-8839", "clpid": "Iverson-Joseph-Kramer" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Painter", "given_name": "Oskar J.", "orcid": "0000-0002-1581-9209", "clpid": "Painter-O" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis is concerned with fault-tolerant quantum information processing using quantum error-correcting codes. It contains two major pieces of work. The first is a study of coherent noise in the context of stabilizer error-correcting codes. The second is a proposed scheme for a universal set of fault-tolerant logical gates in a particular code family built out of the 3D toric code.
\r\n \r\nChapter 1 provides an introduction to quantum computation and fault tolerance. Many basic concepts in error-correcting codes are defined. Special attention is paid to the set of code properties that are most likely to determine how easily a given fault-tolerant scheme might be implemented on a physical device. These include the fault-tolerant noise threshold and the overhead.
\r\n \r\nIn Chapters 2 and 3 we study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to coherent errors may increase quadratically with the circuit size; in contrast, when errors are incoherent (for example, depolarizing noise), the average infidelity increases at worst linearly with circuit size. We consider the performance of quantum stabilizer codes against a noise model in which a unitary rotation is applied to each qubit, where the axes and angles of rotation are nearly the same for all qubits. In Chapter 2 we introduce coherent noise and incoherent noise and a number of methods that are useful for the study of coherent noise. We study the repetition code as a basic example, and we also study a correlated noise model. In Chapter 3 we show that for the toric code subject to such independent coherent noise, and for minimal-weight decoding, the logical channel after error correction becomes increasingly incoherent as the length of the code increases, provided the noise strength decays inversely with the code distance. A similar conclusion holds for weakly correlated coherent noise. Our methods can also be used for analyzing the performance of other codes and fault-tolerant protocols against coherent noise. However, our result does not show that the coherence of the logical channel is suppressed in the more physically relevant case where the noise strength is held constant as the code block grows, and we recount the difficulties that prevented us from extending the result to that case. Nevertheless our work supports the idea that fault-tolerant quantum computing schemes will work effectively against coherent noise, providing encouraging news for quantum hardware builders who worry about the damaging effects of control errors and coherent interactions with the environment.
\r\n \r\nChapter 4 is connected to another aspect of fault tolerance, fault-tolerant logical gates. The toric code is a promising candidate for fault-tolerant quantum computation because of its high threshold and low-weight stabilizers. A universal gate set in the toric code generally requires magic state distillation, which can incur a significant qubit overhead. In this work we construct an error-correcting code in three dimensions based on the toric code that features a fault-tolerant T gate with no magic state distillation required. We further describe a subsystem version of our code which supports a universal set of fault-tolerant gates. This code can be converted into the stabilizer version using gauge-fixing. We also argue that our code can be converted to a (2+1)-D protocol, where a 2D lattice undergoes a measurement-based protocol over time. In this way, a fault-tolerant logical T gate can be realized in a 2D toric code structure.
", "doi": "10.7907/q5ev-rm81", "publication_date": "2020", "thesis_type": "phd", "thesis_year": "2020" }, { "id": "thesis:11011", "collection": "thesis", "collection_id": "11011", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06022018-013547962", "primary_object_url": { "basename": "maguire_shaun_2018a.pdf", "content": "final", "filesize": 5856125, "license": "other", "mime_type": "application/pdf", "url": "/11011/15/maguire_shaun_2018a.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "The Spectral Theory of Multiboundary Wormholes", "author": [ { "family_name": "Maguire", "given_name": "Shaun Cohn", "orcid": "0000-0003-3917-8562", "clpid": "Maguire-Shaun-Cohn" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Painter", "given_name": "Oskar J.", "orcid": "0000-0002-1581-9209", "clpid": "Painter-O" }, { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "This thesis introduces a new phase transitions in three dimensional quantum gravity. The main technical tools comes from the spectral theory of hyperbolic manifolds.", "doi": "10.7907/W8HM-4Y42", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:10942", "collection": "thesis", "collection_id": "10942", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05262018-061607919", "primary_object_url": { "basename": "Yunger_Halpern_Nicole_2018_Thesis.pdf", "content": "final", "filesize": 6487815, "license": "other", "mime_type": "application/pdf", "url": "/10942/1/Yunger_Halpern_Nicole_2018_Thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Quantum Steampunk: Quantum Information, Thermodynamics, Their Intersection, and Applications Thereof Across Physics", "author": [ { "family_name": "Yunger Halpern", "given_name": "Nicole", "orcid": "0000-0001-8670-6212", "clpid": "Yunger-Halpern-Nicole" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Endres", "given_name": "Manuel A.", "orcid": "0000-0002-4461-224X", "clpid": "Endres-M" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "Combining quantum information theory (QIT) with thermodynamics unites 21st-century technology with 19th-century principles. The union elucidates the spread of information, the flow of time, and the leveraging of energy. This thesis contributes to the theory of quantum thermodynamics, particularly to QIT thermodynamics. The thesis also contains applications of the theory, wielded as a toolkit, across physics. Fields touched on include atomic, molecular, and optical physics; nonequilibrium statistical mechanics; condensed matter; high-energy physics; and chemistry. I propose the name quantum steampunk for this program. The term derives from the steampunk genre of literature, art, and cinema that juxtaposes futuristic technologies with 19th-century settings.
", "doi": "10.7907/96EJ-N815", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:10954", "collection": "thesis", "collection_id": "10954", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05282018-130631568", "primary_object_url": { "basename": "chatwin-davies_aidan_2018_thesis.pdf", "content": "final", "filesize": 2184556, "license": "other", "mime_type": "application/pdf", "url": "/10954/1/chatwin-davies_aidan_2018_thesis.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Gravity Informed", "author": [ { "family_name": "Chatwin-Davies", "given_name": "Aidan \u00c9mile", "orcid": "0000-0003-1406-9271", "clpid": "Chatwin-Davies-Aidan-\u00c9mile" } ], "thesis_advisor": [ { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" } ], "thesis_committee": [ { "family_name": "Cheung", "given_name": "Clifford W.", "orcid": "0000-0002-9983-9425", "clpid": "Cheung-Clifford" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Weinstein", "given_name": "Alan Jay", "orcid": "0000-0002-0928-6784", "clpid": "Weinstein-Alan-J-Physics" }, { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" } ], "local_group": [ { "literal": "Walter Burke Institute for Theoretical Physics" }, { "literal": "div_pma" } ], "abstract": "Formulating a universally satisfactory theory of quantum gravity is a long-standing open problem in theoretical physics. Relatively recently, the use of techniques from quantum information has emerged as a powerful tool for analyzing phenomena that lie at the intersection of quantum theory and gravitation. This thesis describes several advances and novel proposals that were made regarding information theoretic aspects of quantum gravity in three broad areas: holography, cosmology, and the black hole information problem.
\r\n\r\nRegarding holography, we first assess the differences between typical holographic states and fully random states. Next, we show that determining Ryu-Takayanagi surfaces in AdS3/CFT2 is computationally easy from a complexity-theoretic standpoint. Finally, we identify precise consistency conditions that constrain the validity of an early tensor network model for the AdS/CFT correspondence that uses the Multiscale Entanglement Renormalization Ansatz (MERA).
\r\n\r\nRegarding cosmology, we propose an alternative interpretation of the MERA as a discretization of de Sitter spacetime. Next, we return to holographic ideas and show that an appropriately-defined Generalized Second Law implies a cosmic no-hair theorem for certain classes of cosmological spacetimes. Finally, we advance an information-theoretic proposal for calculating the signature of a quantum gravity-motivated, fully covariant, natural ultraviolet cutoff in the spectrum of inflationary perturbations.
\r\n\r\nRegarding the black hole information problem, we begin by exhibiting a simple protocol which, under highly specific circumstances, allows one to retrieve a single qubit from a black hole. Next, we propose an operational resolution of the black hole information problem in which observers who enter the black hole could never detect an inconsistency between their experiences and quantum mechanics due to the finite amount of time available before reaching the central singularity. Finally, we discuss a proposal to understand the emergence of an ensemble of definite geometries during the process of black hole evaporation as a decoherence process, as well as its implications for the black hole information problem.
", "doi": "10.7907/ZD4W-4C63", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:10955", "collection": "thesis", "collection_id": "10955", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05282018-173928314", "primary_object_url": { "basename": "Kubica2018.pdf", "content": "final", "filesize": 6379501, "license": "other", "mime_type": "application/pdf", "url": "/10955/1/Kubica2018.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "The ABCs of the Color Code: A Study of Topological Quantum Codes as Toy Models for Fault-Tolerant Quantum Computation and Quantum Phases Of Matter", "author": [ { "family_name": "Kubica", "given_name": "Aleksander Marek", "orcid": "0000-0001-8213-8190", "clpid": "Kubica-Aleksander-Marek" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "This thesis is devoted to studying a class of quantum error-correcting codes \u2014 topological quantum codes. We explore the question of how one can achieve fault- tolerant quantum computation with topological codes. We treat quantum error-correcting codes not only as a compelling ingredient needed to build a quantum computer, but also as a useful theoretical tool in other areas of physics. In particular, we explore what insights topological codes can provide into challenging questions, such as the classification of quantum phases of matter.
\r\n\r\nIn this thesis, we focus on a family of topological codes \u2014 color codes, which are particularly intriguing due to the rich physics they display and their computational power. We start by introducing color codes and explaining their basic properties. Then, we show how to perform fault-tolerant universal quantum computation with three-dimensional color codes by transverse gates and code switching. We later compare the resource overhead of the code-switching approach with that of a state distillation scheme. We discuss how to perform error correction with the toric and color codes, as well as introduce local decoders for those two families of codes. By exploiting a connection between error correction and statistical mechanics we estimate the storage threshold error rates for bit-flip and phase-flip noise in the three-dimensional color code. We finish by showing that the color and toric code families in d dimensions are equivalent in a sense of local unitary transformations and explore implications of this equivalence.
", "doi": "10.7907/059V-MG69", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:10860", "collection": "thesis", "collection_id": "10860", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05082018-133854488", "type": "thesis", "title": "Towards a Theory of Quantum Gravity Through Geometrization of Quantum Mechanics", "author": [ { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" } ], "thesis_advisor": [ { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Cheung", "given_name": "Clifford W.", "orcid": "0000-0002-9983-9425", "clpid": "Cheung-Clifford" }, { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" }, { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "In this thesis, we adapt an approach by assuming quantum mechanics as a fundamental theory of nature and attempt to recover familiar concepts such as space-time geometry and gravity from quantum wavefunctions and their unitary evolutions. More specifically, we explore a number of approaches in \"geometrizing\" quantum systems using techniques such as tensor networks and manifold learning. We find that consistency conditions in quantum gravity can be used to put constraints on tensor network models that approximate the anti-de Sitter/Conformal Field Theory correspondence. Furthermore, quantum circuits and tensor networks can also be used to describe cosmological models and reproduce important features of space-time configurations such as de Sitter space. We find that a generic framework using quantum circuit to describe cosmology puts an upper bound on the number of e-folds during the inflationary phase of the Universe's expansion. In addition to tensor network models, we also propose a Bulk Entanglement Gravity framework that analyzes the entanglement data of a quantum state in a Hilbert space without any a priori assumptions on geometry, such as the likes of a boundary conformal field theory. We find that from an amorphous configuration, one can directly recover geometry of bulk space-time from a generic class of wavefunctions that is fully characterized in this thesis via quantum entropy cone techniques. We find that under a number of assumptions, it is possible to derive linearized Einstein's equation from a version of Jacobson's entanglement equilibrium conditions for an emergent spacetime geometry in the weak field limit near Minkowski space. We show that non-local entanglement perturbations display features of wormhole-like configurations. We also clarify connections between Bulk Entanglement Gravity and highly generic features in quantum error correction codes that can be used to derive gravity.
", "doi": "10.7907/SCD0-VB49", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:10981", "collection": "thesis", "collection_id": "10981", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05312018-124004005", "type": "thesis", "title": "The Union of Quantum Field Theory and Non-Equilibrium Thermodynamics", "author": [ { "family_name": "Bartolotta", "given_name": "Anthony Leo", "orcid": "0000-0003-4971-9545", "clpid": "Bartolotta-Anthony-Leo" } ], "thesis_advisor": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" } ], "thesis_committee": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Schwab", "given_name": "Keith C.", "orcid": "0000-0001-8216-4815", "clpid": "Schwab-K-C" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "Walter Burke Institute for Theoretical Physics" }, { "literal": "div_pma" } ], "abstract": "Quantum field theory is the language used to describe nature at its most fundamental scales; while thermodynamics is a framework to describe the collective behavior of macroscopic systems. Recent advances in non-equilibrium thermodynamics have enabled this framework to be applied to smaller systems operating out of thermal equilibrium. This thesis is concerned with both quantum field theory and non-equilibrium thermodynamics independently and with their intersection.
\r\n\r\nFirst, a purely phenomenological application of quantum field theory is explored in the context of the upcoming Mu2E experiment. This experiment will look for rare decays which would indicate the presence of physics beyond the Standard Model. Using the language of effective field theories, a next-to-leading order analysis of the conversion rate is performed.
\r\n\r\nThe focus then shifts to an apparent paradox in the Bayesian interpretation of statistical mechanics. For a Bayesian observer making measurements of an open system, the Shannon entropy decreases, in apparent violation of the Second Law of Thermodynamics. It is shown that rather than utilizing the entropy, which can decrease under Bayesian updates, the Second Law for a Bayesian observer can be rephrased in terms\r\nof a cross-entropy which is always non-negative.
\r\n\r\nFinally, the intersection of quantum field theory and non-equilibrium thermodynamics is examined. Using quantum work fluctuation theorems, an investigation of how these frameworks can be applied to a driven quantum field theory is performed. For a time-dependent variant of \u03bb\u03c64 , analytic expressions for the work distribution functions at one-loop order are derived. These expressions are shown to satisfy the quantum Jarzynski equality and Crooks fluctuation theorem.
", "doi": "10.7907/F7VT-7X41", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:10992", "collection": "thesis", "collection_id": "10992", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05312018-184631141", "primary_object_url": { "basename": "fishman_matthew_2018.pdf", "content": "updated", "filesize": 1341193, "license": "other", "mime_type": "application/pdf", "url": "/10992/28/fishman_matthew_2018.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Development of Tensor Network Algorithms for Studying Classical and Quantum Many-Body Systems", "author": [ { "family_name": "Fishman", "given_name": "Matthew Theodore", "clpid": "Fishman-Matthew-Theodore" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "White", "given_name": "Steven R.", "clpid": "White-S-R" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "White", "given_name": "Steven R.", "clpid": "White-S-R" }, { "family_name": "Chan", "given_name": "Garnet K.", "orcid": "0000-0001-8009-6038", "clpid": "Chan-G-K" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "The field of tensor networks, kicked off in 1992 by Steve White's invention of the spectacularly successful density matrix renormalization group (DMRG) algorithm, has exploded in popularity in recent years. Tensor networks are poised to play a role in helping us solve some of the greatest open physics problems of our time, such as understanding the nature of high-temperature superconductivity and illuminating a theory of quantum gravity. DMRG and extensions based on a class of variational states known as tensor network states have been indispensable tools in helping us understand both numerically and theoretically the properties of complicated classical and quantum many-body systems. However, practical challenges to these techniques still remain, and algorithmic developments are needed before tensor network algorithms can be applied to more physics problems. In this thesis we present a variety of recent advancements to tensor network algorithms.
\r\n\r\nFirst we describe a DMRG-like algorithm for noninteracting fermions. Noninteracting fermions, naturally being gapless and therefore having high levels of entanglement, are actually a challenging setting for standard DMRG algorithms, and we believe this new algorithm can help with tensor network calculations in that setting.
\r\n\r\nNext we explain a new algorithm called the variational uniform matrix product state (VUMPS) algorithm that is a DMRG-like algorithm that works directly in the thermodynamic limit, improving upon currently available MPS-based methods for studying infinite 1D and quasi-1D quantum many-body systems.
\r\n\r\nFinally, we describe a variety of improvements to algorithms for contracting 2D tensor networks, a common problem in tensor network algorithms, for example for studying 2D classical statistical mechanics problems and 2D quantum many-body problems with projected entangled pair states (PEPS). One is a new variant of the corner transfer matrix renormalization group (CTMRG) algorithm of Nishino and Okunishi that improves the numerical stability for contracting asymmetric two-dimensional tensor networks compared to the most commonly used method. Another is the application of the VUMPS algorithm to contracting 2D tensor networks. The last is a new alternative to CTMRG, where the tensors are solved for with eigenvalue equations instead of a power method, which we call the fixed point corner method (FPCM). We present results showing the transfer matrix VUMPS algorithm and FPCM significantly improve upon the convergence time of CTMRG. We expect these algorithms will play an important role in expanding the set of 2D classical and 2D quantum many-body problems that can be addressed with tensor networks.
", "doi": "10.7907/44s6-0q68", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:11002", "collection": "thesis", "collection_id": "11002", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06012018-143029746", "type": "thesis", "title": "Chaos and Randomness in Strongly-Interacting Quantum Systems", "author": [ { "family_name": "Hunter-Jones", "given_name": "Nicholas R.", "clpid": "Hunter-Jones-Nicholas-R" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" }, { "family_name": "Simmons-Duffin", "given_name": "David", "orcid": "0000-0002-2937-9515", "clpid": "Simmons-Duffin-D" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "Quantum chaos entails an entropic and computational obstruction to describing a system and thus is intrinsically difficult to characterize. An understanding of quantum chaos is fundamentally related to the mechanism of thermalization in many-body systems and the quantum nature of black holes. In this thesis we adopt the view that quantum information theory provides a powerful framework in which to elucidate chaos in strongly-interacting quantum systems.
\r\n\r\nWe first push towards a more precise understanding of chaotic dynamics by relating different diagnostics of chaos, studying the time-evolution of random matrix Hamiltonians, and quantifying random matrix behavior in physical systems. We derive relations between out-of-time ordered correlation functions, spectral quantities, and frame potentials to relate the scrambling of quantum information, decay of correlators, and Haar-randomness. We give analytic expressions for these quantities in random matrix theory to explore universal aspects of late-time dynamics. Motivated by our random matrix results, we define k-invariance in order to capture the onset of random matrix behavior in physical systems.
\r\n\r\nWe then refine our diagnostics in order to study chaotic systems with symmetry by considering Haar-randomness with respect to quotients of the unitary group, and in doing so we generalize our quantum information machinery. We further consider extended random matrix ensembles in the context of strongly-interacting quantum systems dual to black holes. Lastly, we study operator growth in classes of random quantum circuits.
", "doi": "10.7907/BHZ5-HV76", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:10926", "collection": "thesis", "collection_id": "10926", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05232018-150514177", "primary_object_url": { "basename": "KomarAnna2018.pdf", "content": "final", "filesize": 16282237, "license": "other", "mime_type": "application/pdf", "url": "/10926/1/KomarAnna2018.pdf", "version": "v6.0.0" }, "type": "thesis", "title": "Quantum Computation and Information Storage in Quantum Double Models", "author": [ { "family_name": "K\u00f3m\u00e1r", "given_name": "Anna", "orcid": "0000-0002-4701-4931", "clpid": "K\u00f3m\u00e1r-Anna" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Endres", "given_name": "Manuel A.", "orcid": "0000-0002-4461-224X", "clpid": "Endres-M" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "The results of this thesis concern the real-world realization of quantum computers, specifically how to build their \"hard drives\" or quantum memories. These are many-body quantum systems, and their building blocks are qubits, the same way bits are the building blocks of classical computers.
\r\n\r\nQuantum memories need to be robust against thermal noise, noise that would otherwise destroy the encoded information, similar to how strong magnetic field corrupts data classically stored in magnetic many-body systems (e.g., in hard drives). In this work I focus on a subset of many-body models, called quantum doubles, which, in addition to storing the information, could be used to perform the steps of the quantum computation, i.e., work as a \"quantum processor\".
\r\n\r\nIn the first part of my thesis, I investigate how long a subset of quantum doubles (qudit surface codes) can retain the quantum information stored in them, referred to as their memory time. I prove an upper bound for this memory time, restricting the maximum possible performance of qudit surface codes.
\r\n\r\nThen, I analyze the structure of quantum doubles, and find two interesting properties. First, that the high-level description of doubles, utilizing only their quasi-particles to describe their states, disregards key components of their microscopic properties. In short, quasi-particles (anyons) of quantum doubles are not in a one-to-one correspondence with the energy eigenstates of their Hamiltonian. Second, by investigating phase transitions of a simple quantum double, D(S3), I map its phase diagram, and interpret the physical processes the theory undergoes through terms borrowed from the Landau theory of phase transitions.
", "doi": "10.7907/KMJ2-1307", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:10432", "collection": "thesis", "collection_id": "10432", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09122017-161101236", "primary_object_url": { "basename": "thesis_shukla_sujeet_2017_v1.pdf", "content": "final", "filesize": 6464183, "license": "other", "mime_type": "application/pdf", "url": "/10432/1/thesis_shukla_sujeet_2017_v1.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Tensor Network Representation of Many-Body Quantum States and Unitary Operators", "author": [ { "family_name": "Shukla", "given_name": "Sujeet Kumar", "orcid": "0000-0002-4283-536X", "clpid": "Shukla-Sujeet-Kumar" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" }, { "family_name": "Vidick", "given_name": "Thomas G.", "orcid": "0000-0002-6405-365X", "clpid": "Vidick-T" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "Understanding many-body quantum systems is one of the most challenging problems in contemporary condensed-matter physics. Tensor network representation of quantum states and operators are taking central stage in this pursuit and beyond. They prove to be a powerful numerical and conceptual tool, and indeed a new language altogether. This thesis investigates various aspects of these representations by focusing on two specific problems: the first half of the thesis is devoted to examining how 'stable' a tensor network representation is for two-dimensional quantum states with topological order, and the second half explores the representability of various unitary loop operators with tensor networks.
\r\n\r\nIn the numerical usage of the tensor networks, the tensor is varied as to find the representation of the ground states of the given Hamiltonian. In chapter two and three of this thesis we show that such a numerical program for topological phases can be 'ill-posed'. We show that tensor network can be an unstable representation for a topological phase: even an infinitesimal variation in the representation results in the loss of topological order, completely or partially. We diagnose this problem by identifying the exact causes of this instability, and find that it is only tensor variations in certain directions that result in instability, because they result in the condensation of bosonic quasi-particles of the phase. Such unstable variations are characterized by two properties: (1) they can replace a tensor in the tensor network without making the network collapse, and (2) their presence in the network represents the presence of a non-trivial topological charge. We prove that the general tensor representation of all string-net models suffer with such instabilities. We propose an exact mathematical operator to project out all such unstable variations and show its efficacy for a few models by direct calculations. Such an operator can be useful in numerical programs involving such tensor representations. We also point out that such variations play a crucial role in simulating topological phase transitions and their presence can be vital in an accurate simulation.
\r\n\r\nIn chapter four and five of this thesis we focus on the representability of unitary loop operators by tensor networks. Such operators not only provide an important tool in the study of dynamical process in one-dimensional systems, but also in understanding and classification of symmetry protected topological phases in two dimensions. To characterize all such operators, we find a necessary and sufficient condition for any loop tensor network operator of a given length to represent a unitary operator. In particular, it is shown that all unitary operators that map local operators to local operators (locality-preserving) can always be represented by a tensor network. Locality-preserving unitary loop operators are classified by a rational index called the GNVW index defined in Ref. [1] which measures how much information 'flows' along the loop. We define Rank-Ratio index for tensor network operators and show that it is completely equivalent to the GNVW index. Therefore, GNVW index of a unitary operator can be easily extracted from its tensor network representation. We find that, other than representing locality-preserving unitary maps, tensor networks can also represent unitary operators that map local operators to global (non-local) operators. These tensor network operators are found to have a long-ranged order similar to tensors that represent topological tensor network states in two dimensions.
", "doi": "10.7907/Z9DF6PDB", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:10286", "collection": "thesis", "collection_id": "10286", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06052017-155729766", "primary_object_url": { "basename": "Evgeny_Mozgunov_2017.pdf", "content": "final", "filesize": 2037307, "license": "cc_by_nc_sa", "mime_type": "application/pdf", "url": "/10286/2/Evgeny_Mozgunov_2017.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Slow Drive of Many-Body Localized Systems", "author": [ { "family_name": "Mozgunov", "given_name": "Evgeny", "clpid": "Mozgunov-Evgeny" } ], "thesis_advisor": [ { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" } ], "thesis_committee": [ { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" }, { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "We investigate a many-body localized 1d spin chain with a Hamiltonian consisting of classical disordered Ising and a small transversal field. An existing perturbative diagonalization by Imbrie is simplified and reinterpreted in order to prove the anticipated form of the Lieb-Robinson bound and the area law in an eigenstate. We also show how to approximately reduce Imbrie\u2019s unitary to a finite depth circuit. The concept of resonances in Imbrie\u2019s work can be given a physical meaning as an avoided crossing of levels as functions of a magnetic field. For a slow drive of this field, we discuss the proofs of validity for an efficient classical simulation of such disordered systems, both isolated and in contact with the environment. Our results are applicable to Floquet systems and describe an unexpected mechanism of heating up over long times. We also revisit noisy quantum adiabatic annealers like the D-wave machine and find a nontrivial physics that can possibly be observed in them.
", "doi": "10.7907/Z9DJ5CND", "publication_date": "2017", "thesis_type": "phd", "thesis_year": "2017" }, { "id": "thesis:9854", "collection": "thesis", "collection_id": "9854", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06072016-162802972", "type": "thesis", "title": "Toward Realizable Quantum Computers", "author": [ { "family_name": "Beverland", "given_name": "Michael Edward", "orcid": "0000-0003-0954-4509", "clpid": "Beverland-Michael-Edward" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "The work in this thesis splits naturally into two parts: (1) experimentally oriented work consisting of experimental proposals for systems that could be used to implement quantum information tasks with current technology, and (2) theoretical work focusing on universal fault-tolerant quantum computers which we hope can be scaled as experimental capabilities continue to move forward. ", "doi": "10.7907/Z96M34SC", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:8184", "collection": "thesis", "collection_id": "8184", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04082014-225653991", "primary_object_url": { "basename": "Fornal_Bartosz_2014_thesis.pdf", "content": "final", "filesize": 2552701, "license": "other", "mime_type": "application/pdf", "url": "/8184/1/Fornal_Bartosz_2014_thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Baryon Number Violation beyond the Standard Model", "author": [ { "family_name": "Fornal", "given_name": "Bartosz", "clpid": "Fornal-Bartosz" } ], "thesis_advisor": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" } ], "thesis_committee": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" }, { "family_name": "Politzer", "given_name": "Hugh David", "orcid": "0000-0002-4983-6621", "clpid": "Politzer-H-D" }, { "family_name": "Porter", "given_name": "Frank C.", "orcid": "0000-0003-1948-8889", "clpid": "Porter-F-C" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "This thesis describes simple extensions of the standard model with new sources of baryon number violation but no proton decay. The motivation for constructing such theories comes from the shortcomings of the standard model to explain the generation of baryon asymmetry in the universe, and from the absence of experimental evidence for proton decay. However, lack of any direct evidence for baryon number violation in general puts strong bounds on the naturalness of some of those models and favors theories with suppressed baryon number violation below the TeV scale. The initial part of the thesis concentrates on investigating models containing new scalars responsible for baryon number breaking. A model with new color sextet scalars is analyzed in more detail. Apart from generating cosmological baryon number, it gives nontrivial predictions for the neutron-antineutron oscillations, the electric dipole moment of the neutron, and neutral meson mixing. The second model discussed in the thesis contains a new scalar leptoquark. Although this model predicts mainly lepton flavor violation and a nonzero electric dipole moment of the electron, it includes, in its original form, baryon number violating nonrenormalizable dimension-five operators triggering proton decay. Imposing an appropriate discrete symmetry forbids such operators. Finally, a supersymmetric model with gauged baryon and lepton numbers is proposed. It provides a natural explanation for proton stability and predicts lepton number violating processes below the supersymmetry breaking scale, which can be tested at the Large Hadron Collider. The dark matter candidate in this model carries baryon number and can be searched for in direct detection experiments as well. The thesis is completed by constructing and briefly discussing a minimal extension of the standard model with gauged baryon, lepton, and flavor symmetries.", "doi": "10.7907/R0MY-VR06", "publication_date": "2014", "thesis_type": "phd", "thesis_year": "2014" }, { "id": "thesis:8443", "collection": "thesis", "collection_id": "8443", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05302014-131308138", "primary_object_url": { "basename": "bfefferman-thesis-OUT.pdf", "content": "final", "filesize": 432380, "license": "other", "mime_type": "application/pdf", "url": "/8443/1/bfefferman-thesis-OUT.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "The Power of Quantum Fourier Sampling", "author": [ { "family_name": "Fefferman", "given_name": "William Jason", "orcid": "0000-0002-9627-0210", "clpid": "Fefferman-William-Jason" } ], "thesis_advisor": [ { "family_name": "Umans", "given_name": "Christopher M.", "orcid": "0000-0002-6390-9401", "clpid": "Umans-C-M" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" } ], "thesis_committee": [ { "family_name": "Umans", "given_name": "Christopher M.", "orcid": "0000-0002-6390-9401", "clpid": "Umans-C-M" }, { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_eng" } ], "abstract": "How powerful are Quantum Computers? Despite the prevailing belief that Quantum Computers are more powerful than their classical counterparts, this remains a conjecture backed by little formal evidence. Shor's famous factoring algorithm [Shor97] gives an example of a problem that can be solved efficiently on a quantum computer with no known efficient classical algorithm. Factoring, however, is unlikely to be NP-Hard, meaning that few unexpected formal consequences would arise, should such a classical algorithm be discovered. Could it then be the case that any quantum algorithm can be simulated efficiently classically? Likewise, could it be the case that Quantum Computers can quickly solve problems much harder than factoring? If so, where does this power come from, and what classical computational resources do we need to solve the hardest problems for which there exist efficient quantum algorithms?
\r\n\r\nWe make progress toward understanding these questions through studying the relationship between classical nondeterminism and quantum computing. In particular, is there a problem that can be solved efficiently on a Quantum Computer that cannot be efficiently solved using nondeterminism? In this thesis we address this problem from the perspective of sampling problems. Namely, we give evidence that approximately sampling the Quantum Fourier Transform of an efficiently computable function, while easy quantumly, is hard for any classical machine in the Polynomial Time Hierarchy. In particular, we prove the existence of a class of distributions that can be sampled efficiently by a Quantum Computer, that likely cannot be approximately sampled in randomized polynomial time with an oracle for the Polynomial Time Hierarchy.
\r\n\r\nOur work complements and generalizes the evidence given in Aaronson and Arkhipov's work [AA2013] where a different distribution with the same computational properties was given. Our result is more general than theirs, but requires a more powerful quantum sampler.
\r\n", "doi": "10.7907/6HJB-MC69", "publication_date": "2014", "thesis_type": "phd", "thesis_year": "2014" }, { "id": "thesis:7763", "collection": "thesis", "collection_id": "7763", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05292013-140541902", "primary_object_url": { "basename": "Haah-thesis.pdf", "content": "final", "filesize": 1704527, "license": "other", "mime_type": "application/pdf", "url": "/7763/1/Haah-thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Lattice Quantum Codes and Exotic Topological Phases of Matter", "author": [ { "family_name": "Haah", "given_name": "Jeongwan", "clpid": "Haah-Jeongwan" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Rains", "given_name": "Eric M.", "orcid": "0000-0002-9915-0919", "clpid": "Rains-E-M" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "This thesis addresses whether it is possible to build a robust memory device for quantum information. Many schemes for fault-tolerant quantum information processing have been developed so far, one of which, called topological quantum computation, makes use of degrees of freedom that are inherently insensitive to local errors. However, this scheme is not so reliable against thermal errors. Other fault-tolerant schemes achieve better reliability through active error correction, but incur a substantial overhead cost. Thus, it is of practical importance and theoretical interest to design and assess fault-tolerant schemes that work well at finite temperature without active error correction.
\r\n\r\nIn this thesis, a three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite temperature is possible, at least to some extent. When quantum information is encoded into a highly entangled ground state of this model and subjected to thermal errors, the errors remain easily correctable for a long time without any active intervention, because a macroscopic energy barrier keeps the errors well localized. As a result, stored quantum information can be retrieved faithfully for a memory time which grows exponentially with the square of the inverse temperature. In contrast, for previously known types of topological quantum storage in three or fewer spatial dimensions the memory time scales exponentially with the inverse temperature, rather than its square.
\r\n\r\nThis spin model exhibits a previously unexpected topological quantum order, in which ground states are locally indistinguishable, pointlike excitations are immobile, and the immobility is not affected by small perturbations of the Hamiltonian. The degeneracy of the ground state, though also insensitive to perturbations, is a complicated number-theoretic function of the system size, and the system bifurcates into multiple noninteracting copies of itself under real-space renormalization group transformations. The degeneracy, the excitations, and the renormalization group flow can be analyzed using a framework that exploits the spin model's symmetry and some associated free resolutions of modules over polynomial algebras.
", "doi": "10.7907/GCYW-ZE58", "publication_date": "2013", "thesis_type": "phd", "thesis_year": "2013" }, { "id": "thesis:7697", "collection": "thesis", "collection_id": "7697", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05102013-172241867", "primary_object_url": { "basename": "Thesis_IsaacKim_Final.pdf", "content": "final", "filesize": 2135749, "license": "other", "mime_type": "application/pdf", "url": "/7697/1/Thesis_IsaacKim_Final.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Conditional Independence in Quantum Many-Body Systems", "author": [ { "family_name": "Kim", "given_name": "Isaac Hyun", "clpid": "Kim-Isaac-Hyun" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "In this thesis, I will discuss how information-theoretic arguments can be used to produce sharp bounds in the studies of quantum many-body systems. The main advantage of this approach, as opposed to the conventional field-theoretic argument, is that it depends very little on the precise form of the Hamiltonian. The main idea behind this thesis lies on a number of results concerning the structure of quantum states that are conditionally independent. Depending on the application, some of these statements are generalized to quantum states that are approximately conditionally independent. These structures can be readily used in the studies of gapped quantum many-body systems, especially for the ones in two spatial dimensions. A number of rigorous results are derived, including (i) a universal upper bound for a maximal number of topologically protected states that is expressed in terms of the topological entanglement entropy, (ii) a first-order perturbation bound for the topological entanglement entropy that decays superpolynomially with the size of the subsystem, and (iii) a correlation bound between an arbitrary local operator and a topological operator constructed from a set of local reduced density matrices. I also introduce exactly solvable models supported on a three-dimensional lattice that can be used as a reliable quantum memory.", "doi": "10.7907/PZJN-A841", "publication_date": "2013", "thesis_type": "phd", "thesis_year": "2013" }, { "id": "thesis:7774", "collection": "thesis", "collection_id": "7774", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05302013-143644943", "primary_object_url": { "basename": "pbrooks-thesis.pdf", "content": "final", "filesize": 5261910, "license": "other", "mime_type": "application/pdf", "url": "/7774/1/pbrooks-thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Quantum Error Correction with Biased Noise", "author": [ { "family_name": "Brooks", "given_name": "Peter Bernard", "clpid": "Brooks-Peter-Bernard" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Brun", "given_name": "Todd A.", "orcid": "0000-0002-8807-3495", "clpid": "Brun-T-A" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "Quantum computing offers powerful new techniques for speeding up the calculation of many classically intractable problems. Quantum algorithms can allow for the efficient simulation of physical systems, with applications to basic research, chemical modeling, and drug discovery; other algorithms have important implications for cryptography and internet security.
\r\n\r\nAt the same time, building a quantum computer is a daunting task, requiring the coherent manipulation of systems with many quantum degrees of freedom while preventing environmental noise from interacting too strongly with the system. Fortunately, we know that, under reasonable assumptions, we can use the techniques of quantum error correction and fault tolerance to achieve an arbitrary reduction in the noise level.
\r\n\r\nIn this thesis, we look at how additional information about the structure of noise, or \"noise bias,\" can improve or alter the performance of techniques in quantum error correction and fault tolerance. In Chapter 2, we explore the possibility of designing certain quantum gates to be extremely robust with respect to errors in their operation. This naturally leads to structured noise where certain gates can be implemented in a protected manner, allowing the user to focus their protection on the noisier unprotected operations.
\r\n\r\nIn Chapter 3, we examine how to tailor error-correcting codes and fault-tolerant quantum circuits in the presence of dephasing biased noise, where dephasing errors are far more common than bit-flip errors. By using an appropriately asymmetric code, we demonstrate the ability to improve the amount of error reduction and decrease the physical resources required for error correction.
\r\n\r\nIn Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled states which decreases as the states are distilled to better quality. The interplay of of these different rates sets limits on the achievable distillation and how quickly states converge to that limit.
", "doi": "10.7907/1TVT-J780", "publication_date": "2013", "thesis_type": "phd", "thesis_year": "2013" }, { "id": "thesis:7898", "collection": "thesis", "collection_id": "7898", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06172013-011507797", "primary_object_url": { "basename": "paul_skerritt_2013_thesis.pdf", "content": "final", "filesize": 1159181, "license": "other", "mime_type": "application/pdf", "url": "/7898/1/paul_skerritt_2013_thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Geometric Quantization and Foliation Reduction", "author": [ { "family_name": "Skerritt", "given_name": "Paul Michael", "clpid": "Skerritt-Paul-Michael" } ], "thesis_advisor": [ { "family_name": "Marsden", "given_name": "Jerrold E.", "clpid": "Marsden-J-E" }, { "family_name": "Desbrun", "given_name": "Mathieu", "orcid": "0000-0003-3424-6079", "clpid": "Desbrun-M" } ], "thesis_committee": [ { "family_name": "Desbrun", "given_name": "Mathieu", "orcid": "0000-0003-3424-6079", "clpid": "Desbrun-M" }, { "family_name": "Marcolli", "given_name": "Matilde", "orcid": "0000-0002-2045-2907", "clpid": "Marcolli-M" }, { "family_name": "Porter", "given_name": "Frank C.", "orcid": "0000-0003-1948-8889", "clpid": "Porter-F-C" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "A standard question in the study of geometric quantization is whether symplectic reduction interacts nicely with the quantized theory, and in particular whether “quantization commutes with reduction.” Guillemin and Sternberg first proposed this question, and answered it in the affirmative for the case of a free action of a compact Lie group on a compact K\u00e4hler manifold. Subsequent work has focused mainly on extending their proof to non-free actions and non-K\u00e4hler manifolds. For realistic physical examples, however, it is desirable to have a proof which also applies to non-compact symplectic manifolds.
\r\n\r\nIn this thesis we give a proof of the quantization-reduction problem for general symplectic manifolds. This is accomplished by working in a particular wavefunction representation, associated with a polarization that is in some sense compatible with reduction. While the polarized sections described by Guillemin and Sternberg are nonzero on a dense subset of the K\u00e4hler manifold, the ones considered here are distributional, having support only on regions of the phase space associated with certain quantized, or \"admissible\", values of momentum.
\r\n\r\nWe first propose a reduction procedure for the prequantum geometric structures that “covers” symplectic reduction, and demonstrate how both symplectic and prequantum reduction can be viewed as examples of foliation reduction. Consistency of prequantum reduction imposes the above-mentioned admissibility conditions on the quantized momenta, which can be seen as analogues of the Bohr-Wilson-Sommerfeld conditions for completely integrable systems.
\r\n\r\nWe then describe our reduction-compatible polarization, and demonstrate a one-to-one correspondence between polarized sections on the unreduced and reduced spaces.
\r\n\r\nFinally, we describe a factorization of the reduced prequantum bundle, suggested by the structure of the underlying reduced symplectic manifold. This in turn induces a factorization of the space of polarized sections that agrees with its usual decomposition by irreducible representations, and so proves that quantization and reduction do indeed commute in this context.
\r\n\r\nA significant omission from the proof is the construction of an inner product on the space of polarized sections, and a discussion of its behavior under reduction. In the concluding chapter of the thesis, we suggest some ideas for future work in this direction.
", "doi": "10.7907/Q72T-Y013", "publication_date": "2013", "thesis_type": "phd", "thesis_year": "2013" }, { "id": "thesis:7071", "collection": "thesis", "collection_id": "7071", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05232012-231713032", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 1220835, "license": "other", "mime_type": "application/pdf", "url": "/7071/1/thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Quantum Nonequilibrium Physics with Rydberg Atoms", "author": [ { "family_name": "Lee", "given_name": "Tony Eilo", "clpid": "Lee-Tony-Eilo" } ], "thesis_advisor": [ { "family_name": "Cross", "given_name": "Michael Clifford", "clpid": "Cross-M-C" } ], "thesis_committee": [ { "family_name": "Cross", "given_name": "Michael Clifford", "clpid": "Cross-M-C" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Painter", "given_name": "Oskar J.", "orcid": "0000-0002-1581-9209", "clpid": "Painter-O" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "A Rydberg atom is an atom excited to a high energy level, and there is a strong dipole-dipole interaction between nearby Rydberg atoms. While there has been much interest in closed systems of Rydberg atoms, less is known about open systems of Rydberg atoms with spontaneous emission. This thesis explores the latter.
\r\n\r\nWe consider a lattice of atoms, laser-excited from the ground state to a Rydberg state and spontaneously decaying back to the ground state. Using mean-field theory, we study the how the steady-state Rydberg population varies across the lattice. There are three phases: uniform, antiferromagnetic, and oscillatory.
\r\n\r\nThen we consider the dynamics of the quantum model when mean-field theory predicts bistability. Over time, the system occasionally jumps between a state of low Rydberg population and a state of high Rydberg population. We explain how entanglement and quantum measurement enable the jumps, which are otherwise classically forbidden.
\r\n\r\nFinally, we let each atom be laser-excited to a short-lived excited state in addition to a Rydberg state. This three-level configuration leads to rich spatiotemporal dynamics that are visible in the fluorescence from the short-lived excited state. The atoms develop strong spatial correlations that change on a long time scale.
", "doi": "10.7907/0N4R-5Y37", "publication_date": "2012", "thesis_type": "phd", "thesis_year": "2012" }, { "id": "thesis:6282", "collection": "thesis", "collection_id": "6282", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04082011-161930834", "primary_object_url": { "basename": "ErsenBilginthesis-oneside.pdf", "content": "final", "filesize": 1548509, "license": "other", "mime_type": "application/pdf", "url": "/6282/1/ErsenBilginthesis-oneside.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Simulation of Strongly Correlated Quantum Many-Body Systems", "author": [ { "family_name": "Bilgin", "given_name": "Ersen", "clpid": "Bilgin-Ersen" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Yeh", "given_name": "Nai-Chang", "orcid": "0000-0002-1826-419X", "clpid": "Yeh-Nai-Chang" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "In this thesis, we address the problem of solving for the properties of interacting quantum many-body systems in thermal equilibrium. The complexity of this problem increases exponentially with system size, limiting exact numerical simulations to very small systems. To tackle more complex systems, one needs to use heuristic algorithms that approximate solutions to these systems. Belief propagation is one such algorithm that we discuss in chapters 2 and 3. Using belief propagation, we demonstrate that it is possible to solve for static properties of highly correlated quantum many-body systems for certain geometries at all temperatures. In chapter 4, we generalize the multiscale renormalization ansatz to the anyonic setting to solve for the ground state properties of anyonic quantum many-body systems. The algorithms we present in chapters 2, 3, and 4 are very successful in certain settings, but they are not applicable to the most general quantum mechanical systems. For this, we propose using quantum computers as we discuss in chapter 5. The dimension reduction algorithm we consider in chapter 5 enables us to prepare thermal states of any quantum many-body system on a quantum computer faster than any previously known algorithm. Using these thermal states as the initialization of a quantum computer, one can study both static and dynamic properties of quantum systems without any memory overhead.", "doi": "10.7907/FQDK-A221", "publication_date": "2011", "thesis_type": "phd", "thesis_year": "2011" }, { "id": "thesis:6477", "collection": "thesis", "collection_id": "6477", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05312011-104108847", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 1153562, "license": "other", "mime_type": "application/pdf", "url": "/6477/1/thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Emerging Paradigms in Quantum Error Correction and Quantum Cryptography", "author": [ { "family_name": "Mandayam Doddamane", "given_name": "Prabha", "clpid": "Mandayam-Doddamane-Prabha" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Painter", "given_name": "Oskar J.", "orcid": "0000-0002-1581-9209", "clpid": "Painter-O" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "We study two novel paradigms in quantum error correction and quantum cryptography \u2014 approximate quantum error correction and noisy-storage cryptography \u2014 which explore alternate approaches for dealing with quantum noise. Approximate quantum error correction seeks to relax the constraint of perfect error correction and construct codes that might be better adapted to correct for specific noise models. Noisy-storage cryptography relies on the power of quantum noise to execute two-party cryptographic tasks securely.
\r\n\r\nMotivated by examples of approximately correcting codes, which make use of fewer physical resources than perfect codes and still obtain comparable levels of fidelity, we study the problem of finding and characterizing such codes in general. We construct for the first time a universal, near-optimal recovery map for approximate quantum error correction (AQEC), with optimality defined in terms of worst-case fidelity. Using the analytical form of this recovery, we also obtain easily verifiable conditions for AQEC. This in turn leads to a simple algorithm for identifying good approximate codes, without having to perform a difficult optimization over all recovery maps for every possible encoding.
\r\n\r\nNoisy-storage cryptography envisions a setting where two-party cryptographic protocols can be securely implemented based solely on the assumption that the quantum storage device possessed by either party is noisy and bounded. Here, we construct two-party protocols (using higher-dimensional states) that are secure even when a dishonest player can store all but a small fraction of the information transmitted during the protocol, in his noiseless quantum memory. We also show that when his memory is noisy, security can be extended to a larger class of noisy quantum memories. Our result demonstrates that the physical limits of the quantum noisy-storage model are indeed achievable, albeit asymptotically.
\r\n\r\nWe also describe our investigations on obtaining strong entropic uncertainty relations using symmetric complementary bases. Uncertainty relations are an important and useful resource in analyzing the security of quantum cryptographic protocols, in addition to being of interest from a foundational standpoint. We present a novel construction of sets of symmetric, complementary bases in dimension d = 2n, which are cyclically permuted under the action of a unitary transformation. We also obtain new lower bounds for uncertainty relations in terms of the min-entropy, which are tight for specific instances of our construction.
", "doi": "10.7907/T8HP-7R18", "publication_date": "2011", "thesis_type": "phd", "thesis_year": "2011" }, { "id": "thesis:5281", "collection": "thesis", "collection_id": "5281", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-09142009-080649", "primary_object_url": { "basename": "Thesis_NHK.pdf", "content": "final", "filesize": 1132168, "license": "other", "mime_type": "application/pdf", "url": "/5281/1/Thesis_NHK.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Information Amidst Noise: Preserved Codes, Error Correction, and Fault Tolerance in a Quantum World", "author": [ { "family_name": "Ng", "given_name": "Hui Khoon", "orcid": "0000-0003-2397-840X", "clpid": "Ng-Hui-Khoon" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Lidar", "given_name": "Daniel", "orcid": "0000-0002-1671-1515", "clpid": "Lidar-D" }, { "family_name": "Chen", "given_name": "Yanbei", "orcid": "0000-0002-9730-9463", "clpid": "Chen-Yanbei" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Quantum coherence is the key ingredient for characteristically quantum effects. It allows for radically different technologies than those using classical systems, including quantum communication, quantum computation, and other devices with quantum control. Quantum coherences are, however, extremely fragile and susceptible to damage from environmental noise. The success of any experiment or technology based on quantum phenomena demands careful preservation of quantum coherences within the system. The study of the effects of noise on a quantum system, and how to prevent loss of coherence is the central theme of this thesis.
\r\n\r\nStarting from basic principles behind how information is stored in a system and what it means for it to be preserved, we build up a framework that allows one to understand what kind of information can survive through a noise process. The resulting elegant matrix-algebraic description of information-preserving structures within a quantum system characterizes codes that can perfectly preserve information in the presence of noise. Our framework encompasses examples like pointer states, noiseless subsystems and error-correcting codes. Furthermore, it leads to a simple, analytical approach to approximate quantum error correction. While perfect quantum error correction is a standard method used to protect information from noise, approximate error correction allows for the use of a smaller quantum system to store the same information, without sacrificing much in resilience against noise.
\r\n\r\nAsking what happens to information stored in a quantum system when the encoding and recovery procedures in error correction are also noisy leads to the concept of fault tolerance. Fault tolerance provides schemes, built upon quantum error correction, that enable accurate simulation of a quantum computation even when the elementary gates are imperfect. Realistic gates used to build a fault-tolerant circuit, however, often require additional noise-suppression techniques in order for any quantum effects to be observed at all. A common technique is dynamical decoupling. We demonstrate how dynamical decoupling in elementary gates can be rigorously accounted for in the fault-tolerance analysis, and show how, under the right conditions, it can lead to fault-tolerant circuits with less stringent noise and resource requirements.
\r\n", "doi": "10.7907/MR2R-FH44", "publication_date": "2010", "thesis_type": "phd", "thesis_year": "2010" }, { "id": "thesis:5256", "collection": "thesis", "collection_id": "5256", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-10302008-115303", "primary_object_url": { "basename": "JDionne_Thesis_Revised.pdf", "content": "final", "filesize": 29193110, "license": "other", "mime_type": "application/pdf", "url": "/5256/1/JDionne_Thesis_Revised.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Flatland Photonics: Circumventing Diffraction with Planar Plasmonic Architectures", "author": [ { "family_name": "Dionne", "given_name": "Jennifer Anne", "orcid": "0000-0001-5287-4357", "clpid": "Dionne-Jennifer-Anne" } ], "thesis_advisor": [ { "family_name": "Atwater", "given_name": "Harry Albert", "orcid": "0000-0001-9435-0201", "clpid": "Atwater-H-A" } ], "thesis_committee": [ { "family_name": "Atwater", "given_name": "Harry Albert", "orcid": "0000-0001-9435-0201", "clpid": "Atwater-H-A" }, { "family_name": "Antonsson", "given_name": "Erik K.", "orcid": "0009-0009-4668-8289", "clpid": "Antonsson-E-K" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Vahala", "given_name": "Kerry J.", "orcid": "0000-0003-1783-1380", "clpid": "Vahala-K-J" }, { "family_name": "Painter", "given_name": "Oskar J.", "orcid": "0000-0002-1581-9209", "clpid": "Painter-O" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "On subwavelength scales, photon-matter interactions are limited by diffraction. The diffraction limit restricts the size of optical devices and the resolution of conventional microscopes to wavelength-scale dimensions, severely hampering our ability to control and probe subwavelength-scale optical phenomena. Circumventing diffraction is now a principle focus of integrated nanophotonics. Surface plasmons provide a particularly promising approach to sub-diffraction-limited photonics. Surface plasmons are hybrid electron-photon modes confined to the interface between conductors and transparent materials. Combining the high localization of electronic waves with the propagation properties of optical waves, plasmons can achieve extremely small mode wavelengths and large local electromagnetic field intensities. Through their unique dispersion, surface plasmons provide access to an enormous phase space of refractive indices and propagation constants that can be readily tuned with material or geometry.
\r\n\r\nIn this thesis, we explore both the theory and applications of dispersion in planar plasmonic architectures. Particular attention is given to the modes of metallic core and plasmon slot waveguides, which can span positive, near-zero, and even negative indices. We demonstrate how such basic plasmonic geometries can be used to develop a suite of passive and active plasmonic components, including subwavelength waveguides, color filters, negative index metamaterials, and optical MOS field effect modulators. Positive index modes are probed by near- and far-field techniques, revealing plasmon wavelengths as small as one-tenth of the excitation wavelength. Negative index modes are characterized through direct visualization of negative refraction. By fabricating prisms comprised of gold, silicon nitride, and silver multilayers, we achieve the first experimental demonstration of a negative index material at visible frequencies, with potential applications for sub-diffraction-limited microscopy and electromagnetic cloaking. We exploit this tunability of complex plasmon mode indices to create a compact metal-oxide-Si (MOS) field effect plasmonic modulator (or plasMOStor). By transforming the MOS gate oxide into an optical channel, amplitude modulation depths of 11.2 dB are achieved in device volumes as small as one one-fifth of a cubic wavelength. Our results indicate the accessibility of tunable refractive indices over a wide frequency band, facilitating design of a new materials class with extraordinary optical properties and applications.
\r\n", "doi": "10.7907/3DCC-CZ57", "publication_date": "2009", "thesis_type": "phd", "thesis_year": "2009" }, { "id": "thesis:1641", "collection": "thesis", "collection_id": "1641", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05052009-133119", "primary_object_url": { "basename": "Template3.pdf", "content": "final", "filesize": 347719, "license": "other", "mime_type": "application/pdf", "url": "/1641/1/Template3.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Applications of Combinatorial Analysis to the Calculation of the Partition Function of the Ising Model", "author": [ { "family_name": "Lin", "given_name": "Ming-Shr Matt", "clpid": "Lin-Ming-Shr-Matt" } ], "thesis_advisor": [ { "family_name": "Wilson", "given_name": "Richard M.", "clpid": "Wilson-R-M" } ], "thesis_committee": [ { "family_name": "Wilson", "given_name": "Richard M.", "clpid": "Wilson-R-M" }, { "family_name": "Wales", "given_name": "David B.", "clpid": "Wales-D-B" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Cross", "given_name": "Michael Clifford", "clpid": "Cross-M-C" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "The research work discussed in this thesis investigated the application of combinatorics and graph theory in the analysis of the partition function of the Ising Model.
\r\n\r\nChapter 1 gives a general introduction to the partition function of the Ising Model and the Feynman Identity in the language of graph theory.
\r\n\r\nChapter 2 describes and proves combinatorially the Feynman Identity in the special case when there is only one vertex and multiple loops.
\r\n\r\nChapter 3 digresses into the number of cycles in a directed graph, along with its application in the special case to derive the analytical expression of the number of non-periodic cycles with positive and negative signs.
\r\n\r\nChapter 4 comes back to the general case of the Feynman Identity. The Feynman Identity is applied to several special cases of the graph and a combinatorial identity is established for each case.
\r\n\r\nChapter 5 concludes the thesis by summarizing the main ideas in each chapter.
\r\n", "doi": "10.7907/RSXD-6W47", "publication_date": "2009", "thesis_type": "phd", "thesis_year": "2009" }, { "id": "thesis:2221", "collection": "thesis", "collection_id": "2221", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05282009-115941", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 1096043, "license": "other", "mime_type": "application/pdf", "url": "/2221/1/thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Foundational Aspects of Nonlocality", "author": [ { "family_name": "Ver Steeg", "given_name": "Gregory Lee", "clpid": "VerSteeg-Gregory-Lee" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Nonlocality refers to correlations between spatially separated parties that are stronger than those explained by the existence of local hidden variables. Quantum mechanics is known to allow some nonlocal correlations between particles in a phenomena known as entanglement. We explore several aspects of nonlocality in general and how they relate to quantum mechanics.
\r\n\r\nFirst, we construct a hierarchy of theories with nonlocal correlations stronger than those allowed in quantum mechanics and derive several results about these theories. We show that these theories include codes that can store an amount of information exponential in the number of physical bits used. We use this result to demonstrate an unphysical consequence of theories with stronger-than-quantum correlations: learning even an approximate description of states in such theories would be practically impossible.
\r\n\r\nNext, we consider the difficult problem of determining whether specific correlations are nonlocal. We present a novel learning algorithm and show that it provides an outer bound on the set of local states, and can therefore be used to identify some nonlocal states.
\r\n\r\nFinally, we put nonlocal correlations to work by showing that the entanglement present in the vacuum of a quantum field can be used to detect spacetime curvature. We quantify how the entangling power of the quantum field varies as a function of spacetime curvature.
", "doi": "10.7907/R7FG-AC54", "publication_date": "2009", "thesis_type": "phd", "thesis_year": "2009" }, { "id": "thesis:2177", "collection": "thesis", "collection_id": "2177", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05272009-130323", "primary_object_url": { "basename": "kovid_thesis.pdf", "content": "final", "filesize": 757959, "license": "other", "mime_type": "application/pdf", "url": "/2177/1/kovid_thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Using Graph States for Quantum Computation and Communication", "author": [ { "family_name": "Goyal", "given_name": "Kovid", "clpid": "Goyal-Kovid" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Yeh", "given_name": "Nai-Chang", "orcid": "0000-0002-1826-419X", "clpid": "Yeh-Nai-Chang" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "In this work, we describe a method to achieve fault tolerant measurement based quantum computation in two and three dimensions. The proposed scheme has an threshold of 7.8*10^-3 and poly-logarithmic overhead scaling. The overhead scaling below the threshold is also studied. The scheme uses a combination of topological error correction and magic state distillation to construct a universal quantum computer on a qubit lattice. The chapters on measurement based quantum computation are written in review form with extensive discussion and illustrative examples.
\r\n\r\nIn addition, we describe and analyze a family of entanglement purification protocols that provide a flexible trade-off between overhead, threshold and output quality. The protocols are studied analytically, with closed form expressions for their threshold.
\r\n", "doi": "10.7907/WR8C-1H18", "publication_date": "2009", "thesis_type": "phd", "thesis_year": "2009" }, { "id": "thesis:3040", "collection": "thesis", "collection_id": "3040", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-08072007-221313", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 1838314, "license": "other", "mime_type": "application/pdf", "url": "/3040/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Dynamics and Simulation of Open Quantum Systems", "author": [ { "family_name": "Zwolak", "given_name": "Michael Philip", "orcid": "0000-0001-6443-7816", "clpid": "Zwolak-Michael-Philip" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Mabuchi", "given_name": "Hideo", "orcid": "0000-0002-5156-7678", "clpid": "Mabuchi-H" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "All systems are open to an essentially uncontrollable environment that acts as a source of decoherence and dissipation. In some cases the environment's only effect is to add a weak relaxation mechanism and thus can be ignored for short timescales. In others, however, the presence of the environment can fundamentally alter the behavior of the system. Such is the case in mesoscopic superconductors where the environment can stabilize superconductivity and in spin-boson systems where the environment induces a localization transition. Likewise, in technological applications we are often interested in systems operating far from equilibrium. Here the environment might act as a particle reservoir or strong driving force.
\r\n\r\nIn all these examples, we need accurate methods to describe the influence of the environment on the system and to solve for the resulting dynamics or equilibrium states. In this thesis, we develop computational and conceptual approaches to efficiently simulate quantum systems in contact with an environment. Our starting point is the use of numerical renormalization techniques. Thus, we restrict our attention to one-dimensional lattices or small quantum systems coupled to an environment. We have developed several complementary algorithms: a superoperator renormalization algorithm for simulating real-time Markovian dynamics and for calculating states in thermal equilibrium; a blocking algorithm for simulating integro-differential equations with long-time memory; and a tensor network algorithm for branched lattices, which can be used to simulate strongly dissipative systems. Further, we provide support for an idea that to generically and accurately simulate the real-time dynamics of strongly dissipative systems, one has to include all or part of the environment within the simulation. In addition, we discuss applications and open questions.
", "doi": "10.7907/565E-JR05", "publication_date": "2008", "thesis_type": "phd", "thesis_year": "2008" }, { "id": "thesis:2447", "collection": "thesis", "collection_id": "2447", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06042007-101617", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 962610, "license": "other", "mime_type": "application/pdf", "url": "/2447/2/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Non-Abelian Anyons and Interferometry", "author": [ { "family_name": "Bonderson", "given_name": "Parsa Hassan", "clpid": "Bonderson-Parsa-Hassan" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Shtengel", "given_name": "Kirill", "orcid": "0000-0002-3857-3141", "clpid": "Shtengel-K" }, { "family_name": "Yeh", "given_name": "Nai-Chang", "orcid": "0000-0002-1826-419X", "clpid": "Yeh-Nai-Chang" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis is primarily a study of the measurement theory of non-Abelian anyons through interference experiments. We give an introduction to the theory of anyon models, providing all the formalism necessary to apply standard quantum measurement theory to such systems. This formalism is then applied to give a detailed analysis of a Mach-Zehnder interferometer for arbitrary anyon models. In this treatment, we find that the collapse behavior exhibited by a target anyon in a superposition of states is determined by the monodromy of the probe anyons with the target. Such measurements may also be used to gain knowledge that would help to properly identify the anyon model describing an unknown system. The techniques used and results obtained from this model interferometer have general applicability, and we use them to also describe the interferometry measurements in a two point-contact interferometer proposed for non-Abelian fractional quantum Hall states. Additionally, we give the complete description of a number of important examples of anyon models, as well as their corresponding quantities that are relevant for interferometry. Finally, we give a partial classification of anyon models with small numbers of particle types.", "doi": "10.7907/5NDZ-W890", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:2022", "collection": "thesis", "collection_id": "2022", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05242007-141715", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 947825, "license": "other", "mime_type": "application/pdf", "url": "/2022/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Unusual Signs in Quantum Field Theory", "author": [ { "family_name": "O'Connell", "given_name": "D\u00f3nal", "orcid": "0000-0001-8886-6391", "clpid": "O'Connell-D\u00f3nal" } ], "thesis_advisor": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" } ], "thesis_committee": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Filippone", "given_name": "Bradley W.", "orcid": "0000-0002-2618-2688", "clpid": "Filippone-B-W" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Ramsey-Musolf", "given_name": "Michael J.", "clpid": "Ramsey-Musolf-M-J" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "Quantum field theory is by now a mature field. Nevertheless, certain physical phenomena remain difficult to understand. This occurs in some cases because well-established quantum field theories are strongly coupled and therefore difficult to solve; in other cases, our current understanding of quantum field theory seems to be inadequate. In this thesis, we will discuss various modifications of quantum field theory which can help to alleviate certain of these problems, either in their own right or as a component of a greater computational scheme. The modified theories we will consider all include unusual signs in some aspect of the theory. We will also discuss limitations on what we might expect to see in experiments, imposed by sign constraints in the customary formulation of quantum field theory.", "doi": "10.7907/FEFB-JZ53", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:1116", "collection": "thesis", "collection_id": "1116", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03252007-155200", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 920188, "license": "other", "mime_type": "application/pdf", "url": "/1116/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Level-Reduction and the Quantum Threshold Theorem", "author": [ { "family_name": "Aliferis", "given_name": "Panagiotis (Panos)", "clpid": "Aliferis-Panagiotis-Panos" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Leung", "given_name": "Debbie W.", "clpid": "Leung-D-W" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Computers have led society to the information age revolutionizing central aspects of our lives from production and communication to education and entertainment. There exist, however, important problems which are intractable with the computers available today and, experience teaches us, will remain so even with the more advanced computers we can envision for tomorrow.
\r\n\r\nQuantum computers promise speedups to some of these important but classically intractable problems. Simulating physical systems, a problem of interest in a diverse range of areas from testing physical theories to understanding chemical reactions, and solving number factoring, a problem at the basis of cryptographic protocols that are used widely today on the internet, are examples of applications for which quantum computers, when built, will offer a great advantage over what is possible with classical computer technology.
\r\n\r\nThe construction of a quantum computer of sufficient scale to solve interesting problems is, however, especially challenging. The reason for this is that, by its very nature, operating a quantum computer will require the coherent control of the quantum state of a very large number of particles. Fortunately, the theory of quantum error correction and fault-tolerant quantum computation gives us confidence that such quantum states can be created, can be stored in memory and can also be manipulated provided the quantum computer can be isolated to a sufficient degree from sources of noise.
\r\n\r\nOne of the central results in the theory of fault-tolerant quantum computation, the quantum threshold theorem shows that a noisy quantum computer can accurately and efficiently simulate any ideal quantum computation provided that noise is weakly correlated and its strength is below a critical value known as the quantum accuracy threshold. This thesis provides a simpler and more transparent non-inductive proof of this theorem based on the concept of level reduction. This concept is also used in proving the quantum threshold theorem for coherent and leakage noise and for quantum computation by measurements. In addition, the proof provides a methodology which allows us to establish improved rigorous lower bounds on the value of the quantum accuracy threshold.
", "doi": "10.7907/3ZM6-HE29", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:2206", "collection": "thesis", "collection_id": "2206", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05282007-231321", "primary_object_url": { "basename": "Thesis.pdf", "content": "final", "filesize": 1347453, "license": "other", "mime_type": "application/pdf", "url": "/2206/1/Thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Topics in General Relativity", "author": [ { "family_name": "Bondarescu", "given_name": "Mihai", "orcid": "0000-0001-8631-0146", "clpid": "Bondarescu-Mihai" } ], "thesis_advisor": [ { "family_name": "Barish", "given_name": "Barry C.", "orcid": "0000-0001-6386-7371", "clpid": "Barish-B-C" }, { "family_name": "Chen", "given_name": "Yanbei", "orcid": "0000-0002-9730-9463", "clpid": "Chen-Yanbei" } ], "thesis_committee": [ { "family_name": "Barish", "given_name": "Barry C.", "orcid": "0000-0001-6386-7371", "clpid": "Barish-B-C" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Chen", "given_name": "Yanbei", "orcid": "0000-0002-9730-9463", "clpid": "Chen-Yanbei" } ], "local_group": [ { "literal": "Astronomy Department" }, { "literal": "div_pma" } ], "abstract": "This thesis is based on three of the five research projects I have worked on during my graduate student years. Each of these projects resulted in a paper a chapter of this thesis is based on. Two other papers I published during my stay at Caltech are not included, as they are not related to the research reported here.
\r\n\r\nAfter a brief introduction in the first chapter, in chapter two I discuss a simple way to greatly reduce tilt instability in Advanced LIGO by changing the mirror shape from nearly-flat previously considered mesa beams to nearly a nearly concentric shape that would provide the beam characteristics without the tilt instability. I also propose a family of hyperboloidal beams that join the nearly-flat and nearly-concentric mesa beams in a continuous manner.
\r\n\r\nIn chapter three I report the results of a recent search for the lowest value of thermal noise that can be achieved in LIGO by changing the mirror shape. I discuss in detail the beam properties and point out some of the characteristics of an advanced LIGO that uses these beams. Such an instrument, if built, would have an event rate roughly three times higher than an advanced LIGO using the Mesa beams introduced in chapter 2.
\r\n\r\nChapter four, which is also the last chapter of this thesis, is based on a Numerical Relativity project. I compute embeddings of general two-dimensional surfaces with spherical topology in flat 3D space using a minimization algorithm. The minimization problem is similar to the one solved in chapter three, albeit in a somewhat different setting.
", "doi": "10.7907/2DKM-A388", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:1953", "collection": "thesis", "collection_id": "1953", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05222007-105100", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 1139633, "license": "other", "mime_type": "application/pdf", "url": "/1953/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Topics in Theoretical Particle Physics and Cosmology", "author": [ { "family_name": "Salem", "given_name": "Michael Phillip", "clpid": "Salem-Michael-Phillip" } ], "thesis_advisor": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" } ], "thesis_committee": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Weinstein", "given_name": "Alan Jay", "orcid": "0000-0002-0928-6784", "clpid": "Weinstein-Alan-J-Physics" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kamionkowski", "given_name": "Marc P.", "orcid": "0000-0001-7018-2055", "clpid": "Kamionkowski-M-P" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "We first delve into particle phenomenology with a study of soft-collinear effective theory (SCET), an effective theory for Quantum Chromodynamics for when all particles are approximately on their light-cones. In particular, we study the matching of SCET(I) involving ultrasoft and collinear particles onto SCET(II) involving soft and collinear particles. We show that the modes in SCET(II) are sufficient to reproduce all of the infrared divergences of SCET(I), a result that was previously in contention.
\r\n\r\nNext we move into early universe cosmology and study alternative mechanisms for generating primordial density perturbations. We study the inhomogeneous reheating mechanism and extend it to describe the scenario where the freeze-out process for a heavy particle is modulated by sub-dominant fields that received fluctuations during inflation. This scenario results in perturbations that are comparable to those generated by the original inhomogeneous reheating scenarios. In addition, we study yet another alternative to single field inflation whereby the curvature perturbation is generated by interactions at the end of inflation, as opposed to when inflaton modes exit the horizon. We clarify the circumstances under which this process can dominate over the standard one and we show that it may result in a spectrum with an observable level of non-Gaussianities.
\r\n\r\nWe then turn to studies of the landscape paradigm, which hypothesizes that the observed universe is just one among a multitude of possibilities that are realized in separate causal regions. Such a landscape has been used to explain the smallness of the cosmological constant, at least when only it scans across the landscape. We study the scenario where both the cosmological constant and the strength of gravity, parameterized by the effective Planck mass, scan across the landscape. We find that selection effects acting on the cosmological constant are significantly weaker in this scenario and we find the measured value of the Planck mass to be exponentially unlikely under certain plausible assumptions about the landscape. Finally, we study some other models of the landscape as part of a possible explanation for quark-sector flavor parameters in the Standard Model. In this picture quark Yukawa couplings result from overlap integrals involving quark and Higgs wavefunctions in compactified extra dimensions, and the values we measure result from random selection from a landscape of possibilities. We find that many of the salient features of the measured flavor parameters are typical of the landscape distribution.
", "doi": "10.7907/BQ6Q-DA17", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:1956", "collection": "thesis", "collection_id": "1956", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05222007-125036", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 748915, "license": "other", "mime_type": "application/pdf", "url": "/1956/1/thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Quantifying Quantum Nonlocality", "author": [ { "family_name": "Toner", "given_name": "Benjamin Francis", "clpid": "Toner-Benjamin-Francis" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Weinstein", "given_name": "Alan Jay", "orcid": "0000-0002-0928-6784", "clpid": "Weinstein-Alan-J-Physics" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Umans", "given_name": "Christopher M.", "orcid": "0000-0002-6390-9401", "clpid": "Umans-C-M" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Quantum mechanics is nonlocal, meaning it cannot be described by any classical local hidden variable model. In this thesis we study two aspects of quantum nonlocality.
\r\n\r\nPart I addresses the question of what classical resources are required to simulate nonlocal quantum correlations. We start by constructing new local models for noisy entangled quantum states. These constructions exploit the connection between nonlocality and Grothendieck's inequality, first noticed by Tsirelson. Next, we consider local models augmented by a limited amount of classical communication. After generalizing Bell inequalities to this setting, we show that (i) one bit of communication is sufficient to simulate the correlations of projective measurements on a maximally entangled state of two qubits, and (ii) five bits of communication are sufficient to simulate the joint correlation of two-outcome measurements on any bipartite quantum state. The latter result can be interpreted as a stronger (constrained) version of Grothendieck's inequality.
\r\n\r\nIn part II, we investigate the monogamy of nonlocal correlations. In a setting where three parties, A, B, and C, share an entangled quantum state of arbitrary dimension, we: (i) bound the trade-off between AB's and AC's violation of the CHSH inequality, obtaining an intriguing generalization of Tsirelson's bound, and (ii) demonstrate that forcing B and C to be classically correlated prevents A and B from violating certain Bell inequalities. We study not only correlations that arise within quantum theory, but also arbitrary correlations that do not allow signaling between separate groups of parties. These results are based on new techniques for obtaining Tsirelson bounds, or bounds on the quantum value of a Bell inequality, and have applications to interactive proof systems and cryptography.
", "doi": "10.7907/69WS-N753", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:2059", "collection": "thesis", "collection_id": "2059", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05252006-185918", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 5419155, "license": "other", "mime_type": "application/pdf", "url": "/2059/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Towards a Quantum Network with Atomic Ensembles", "author": [ { "family_name": "Chou", "given_name": "Chin-wen", "orcid": "0000-0001-7759-823X", "clpid": "Chou-Chin-wen" } ], "thesis_advisor": [ { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" } ], "thesis_committee": [ { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Vahala", "given_name": "Kerry J.", "orcid": "0000-0003-1783-1380", "clpid": "Vahala-K-J" }, { "family_name": "Painter", "given_name": "Oskar J.", "orcid": "0000-0002-1581-9209", "clpid": "Painter-O" }, { "family_name": "Blatt", "given_name": "Rainer", "clpid": "Blatt-R" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "The experiments discussed in this thesis investigate the application of atomic ensembles in building a quantum network. Specifically, the atomic ensembles refer to cesium atoms in magneto-optical traps.
\r\n\r\nChapter 1 gives an introduction to quantum networks, along with the difficulty in extending the range due to the optical loss of communication channels.
\r\n\r\nChapter 2 describes the protocol proposed by Duan, Lukin, Cirac, and Zoller (DLCZ) for overcoming the limit of channel loss on scaling up a quantum network, exploiting relatively simple setups with atomic ensembles. The protocol introduces many capabilities and simplifies many tasks in quantum information processing with atoms and light.
\r\n\r\nChapter 3 summarizes the first step in our lab toward realizing the DLCZ protocol.
\r\n\r\nIn particular, we observed nonclassical correlation between two optical fields generated from one atomic ensemble.
\r\n\r\nChapter 4 is a sidetrack apart from the DLCZ protocol. We demonstrated that the atomic ensemble can be used as a conditional source of single photons. In addition to a description of the experiment, details of the simple model we used to fit the data are also included.
\r\n\r\nChapter 5 augments chapter 4 in that the temporal behavior of the nonclassical correlation is investigated. We found that the correlation decayed rapidly, which is a major obstacle for further implementation of the DLCZ protocol.
\r\n\r\nChapter 6 describes our effort to fight the fast decay of correlation observed in the experiment. A theoretical model is used to better understand the source of decoherence.
\r\n\r\nChapter 7 is the follow-up in the direction of implementing the DLCZ protocol. Two atomic ensembles located in vacuum chambers on two optical tables are entangled in a heralded fashion. The details on controlling the phases of the interferometers and data processing are elaborated.
\r\n\r\nChapter 8 is a practical proposal on how to proceed further toward realization of the DLCZ protocol. Four atomic ensembles are involved in the proposed setup, which merely requires relative phase stability.
\r\n\r\nChapter 9 concludes the thesis and provides several possible directions toward building a large-scale quantum network through the DLCZ protocol.
", "doi": "10.7907/ANAH-0961", "publication_date": "2006", "thesis_type": "phd", "thesis_year": "2006" }, { "id": "thesis:2063", "collection": "thesis", "collection_id": "2063", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05252006-222551", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 580440, "license": "other", "mime_type": "application/pdf", "url": "/2063/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Unification of Quantum Information Theory", "author": [ { "family_name": "Abeyesinghe", "given_name": "Anura Yamesh", "clpid": "Abeyesinghe-Anura-Yamesh" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Mabuchi", "given_name": "Hideo", "orcid": "0000-0002-5156-7678", "clpid": "Mabuchi-H" }, { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "McAfee", "given_name": "R. Preston", "clpid": "McAfee-R-P" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "We present the unification of many previously disparate results in noisy quantum Shannon theory and the unification of all of noiseless quantum Shannon theory. More specifically we deal here with bipartite, unidirectional, and memoryless quantum Shannon theory. We find all the optimal protocols and quantify the relationship between the resources used, both for the one-shot and for the ensemble case, for what is arguably the most fundamental task in quantum information theory: sharing entangled states between a sender and a receiver. We find that all of these protocols are derived from our one-shot superdense coding protocol and relate nicely to each other. We then move on to noisy quantum information theory and give a simple, direct proof of the \"mother\" protocol, or rather her generalization to the Fully Quantum Slepian-Wolf protocol(FQSW). FQSW simultaneously accomplishes two goals: quantum communication-assisted entanglement distillation, and state transfer from the sender to the receiver. As a result, in addition to her other \"children,\" the mother protocol generates the state merging primitive of Horodecki, Oppenheim, and Winter as well as a new class of distributed compression protocols for correlated quantum sources, which are optimal for sources described by separable density operators. Moreover, the mother protocol described here is easily transformed into the so-called \"father\" protocol, demonstrating that the division of single-sender/single-receiver protocols into two families was unnecessary: all protocols in the family are children of the mother.", "doi": "10.7907/XB1H-6193", "publication_date": "2006", "thesis_type": "phd", "thesis_year": "2006" }, { "id": "thesis:1945", "collection": "thesis", "collection_id": "1945", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05222006-153339", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 567871, "license": "other", "mime_type": "application/pdf", "url": "/1945/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Upper and Lower Bounds on Quantum Codes", "author": [ { "family_name": "Smith", "given_name": "Graeme Stewart Baird", "orcid": "0000-0001-8440-3963", "clpid": "Smith-Graeme-Stewart-Baird" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Devetak", "given_name": "Igor", "clpid": "Devetak-I" }, { "family_name": "Smolin", "given_name": "John", "clpid": "Smolin-J" }, { "family_name": "Painter", "given_name": "Oskar J.", "orcid": "0000-0002-1581-9209", "clpid": "Painter-O" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis provides bounds on the performance of quantum error correcting codes when used for quantum communication and quantum key distribution. The first two chapters provide a bare-bones introduction to classical and quantum error correcting codes, respectively. The next four chapters present achievable rates for quantum codes in various scenarios. The final chapter is dedicated to an upper bound on the quantum channel capacity.
\r\n\r\nChapter 3 studies coding for adversarial noise using quantum list codes, showing there exist quantum codes with high rates and short lists. These can be used, together with a very short secret key, to communicate with high fidelity at noise levels for which perfect fidelity is impossible.
\r\n\r\nChapter 4 explores the performance of a family of degenerate codes when used to communicate over Pauli channels, showing they can be used to communicate over almost any Pauli channel at rates that are impossible for a nondegenerate code and that exceed those of previously known degenerate codes. By studying the scaling of the optimal block length as a function of the channel's parameters, we develop a heuristic for designing even better codes.
\r\n\r\nChapter 5 describes an equivalence between a family of noisy preprocessing protocols for quantum key distribution and entanglement distillation protocols whose target state belongs to a class of private states called \"twisted states.\"
\r\n\r\nIn Chapter 6, the codes of Chapter 4 are combined with the protocols of Chapter 5 to provide higher key rates for one-way quantum key distribution than were previously thought possible.
\r\n\r\nFinally, Chapter 7 presents a new upper bound on the quantum channel capacity that is both additive and convex, and which can be interpreted as the capacity of the channel for communication given access to side channels from a class of zero capacity \"cloning\" channels. This \"clone assisted capacity\" is equal to the unassisted capacity for channels that are degradable, which we use to find new upper bounds on the capacity of a depolarizing channel.
", "doi": "10.7907/m0xg-zs21", "publication_date": "2006", "thesis_type": "phd", "thesis_year": "2006" }, { "id": "thesis:2495", "collection": "thesis", "collection_id": "2495", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06072006-174745", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 838808, "license": "other", "mime_type": "application/pdf", "url": "/2495/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "On Quantum Interacting Embedded Geometrical Objects of Various Dimensions", "author": [ { "family_name": "Evnin", "given_name": "Oleg", "orcid": "0000-0001-5999-778X", "clpid": "Evnin-Oleg" } ], "thesis_advisor": [ { "family_name": "Gubser", "given_name": "Steven Scott", "orcid": "0000-0001-5214-1786", "clpid": "Gubser-S-S" }, { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" } ], "thesis_committee": [ { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" }, { "family_name": "Kapustin", "given_name": "Anton N.", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Gukov", "given_name": "Sergei", "orcid": "0000-0002-9486-1762", "clpid": "Gukov-S" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "Modern string theory naturally gives rise to an assortment of dynamical geometrical objects of various dimensions (collectively referred to as \"branes\") embedded into spacetime. The aim of this thesis is to present a series of results (of varying novelty and rigor) pertinent to dynamics of the low-dimensional geometrical objects of this kind. The processes considered are the D0-brane recoil and annihilation, \"local recoil\" of D1-branes (which is a peculiar effect manifested by one-dimensional topological defects in response to an impact, and closely related to soliton recoil), and D- and F-string loop mixing. Apart from the practical relevance within the formalism of string theory, such considerations are worthwhile in that the quantum dynamics of the geometrical objects involved is complex enough to be interesting, yet simple enough to be tractable. Furthermore, some of the results derived here within the string theory formalism may give valuable insights into the dynamics of low-dimensional field-theoretical topological defects.", "doi": "10.7907/1VN2-VZ71", "publication_date": "2006", "thesis_type": "phd", "thesis_year": "2006" }, { "id": "thesis:1722", "collection": "thesis", "collection_id": "1722", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05112005-132038", "primary_object_url": { "basename": "thesis-twoside.pdf", "content": "final", "filesize": 1112069, "license": "other", "mime_type": "application/pdf", "url": "/1722/1/thesis-twoside.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "From Non-Abelian Anyons to Quantum Computation to Coin-Flipping by Telephone", "author": [ { "family_name": "Mochon", "given_name": "Carlos", "clpid": "Mochon-Carlos" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Umans", "given_name": "Christopher M.", "orcid": "0000-0002-6390-9401", "clpid": "Umans-C-M" }, { "family_name": "Mabuchi", "given_name": "Hideo", "orcid": "0000-0002-5156-7678", "clpid": "Mabuchi-H" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Following their divorce, Alice and Bob would like to split some of their possessions by flipping a coin. Unwilling to meet in person, and without a trusted third party, they must figure out a scheme to flip the coin over a telephone that guarantees that neither party can cheat.
\r\n\r\nThe preceding scenario is the traditional definition of two-party coin-flipping. In a classical setting, without limits on the available computational power, one player can always guarantee a coin-flipping victory by cheating. However, by employing quantum communication it is possible to guarantee, with only information-theoretic assumptions, that neither party can win by cheating, with a probability greater than two thirds. Along with the description of such a protocol, this thesis derives a tight lower bound on the bias for a large family of quantum weak coin-flipping protocols, proving such a protocol optimal within the family. The protocol described herein is an improvement and generalization of one examined by Spekkens and Rudolph. The key steps of the analysis involve Kitaev's description of quantum coin-flipping as a semidefinite program whose dual problem provides a certificate that upper bounds the amount of cheating for each party.
\r\n\r\nIn order for such quantum protocols to be viable, though, a number of practical obstacles involving the communication and processing of quantum information must be resolved. In the second half of this thesis, a scheme for processing quantum information is presented, which uses non-abelian anyons that are the magnetic and electric excitations of a discrete-group quantum gauge theory. In particular, the connections between group structure and computational power are examined, generalizing previous work by Kitaev, Ogburn and Preskill. Anyon based computation has the advantage of being topological, which exponentially suppresses the rate of decoherence and the errors associated with the elementary quantum gates. Though no physical systems with such excitations are currently known to exist, it remains an exciting open possibility that such particles could be either engineered or discovered in exotic two-dimensional systems.
", "doi": "10.7907/7JS5-VE50", "publication_date": "2005", "thesis_type": "phd", "thesis_year": "2005" }, { "id": "thesis:2157", "collection": "thesis", "collection_id": "2157", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05272005-160246", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 1900702, "license": "other", "mime_type": "application/pdf", "url": "/2157/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Raman Transitions in Cavity QED", "author": [ { "family_name": "Boozer", "given_name": "Allen David", "clpid": "Boozer-Allen-David" } ], "thesis_advisor": [ { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" } ], "thesis_committee": [ { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" }, { "family_name": "Mabuchi", "given_name": "Hideo", "orcid": "0000-0002-5156-7678", "clpid": "Mabuchi-H" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "In order to study quantum effects such as state superposition and entanglement, one would like to construct simple systems for which the damping rates are slow relative to the rate of coherent evolution. One such system is strong-coupling cavity quantum electrodynamics (QED), in which a single atom is coupled to a single mode of a high finesse optical cavity. In recent years, optical trapping techniques have been applied to the cavity QED system, allowing an individual atom to remain coupled to the cavity for long periods of time. For the purpose of future cavity QED experiments, one would like to gain as much control over the trapped atom as possible; in particular, one would like to cool the center of mass motion of the atom, to measure the magnetic field at the location of the atom, and to be able to prepare the atom in a given internal state. In the first part of this thesis, I present a scheme for driving Raman transitions inside the cavity that can be used to achieve these goals. After giving a detailed theoretical treatment of the Raman scheme, I describe how it can be implemented in the lab and discuss some preliminary experimental results.
\r\n\r\nIn the second part of this thesis, I present a number of simple field theory models. These models were developed in an attempt to understand some of the central ideas of theoretical physics by looking at how the ideas work in a highly simplified context. The hope is that by reducing the mathematical complexity of an actual theory, the underlying physical concepts can be more easily understood.
", "doi": "10.7907/F2WH-X491", "publication_date": "2005", "thesis_type": "phd", "thesis_year": "2005" }, { "id": "thesis:1224", "collection": "thesis", "collection_id": "1224", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03312004-100014", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 566619, "license": "other", "mime_type": "application/pdf", "url": "/1224/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Eigenvalue Inequalities in Quantum Information Processing", "author": [ { "family_name": "Daftuar", "given_name": "Sumit Kumar", "clpid": "Daftuar-Sumit-Kumar" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Damanik", "given_name": "David", "clpid": "Damanik-D" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Wilson", "given_name": "Richard M.", "clpid": "Wilson-R-M" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis develops restrictions governing how a quantum system, jointly held by two parties, can be altered by the local actions of those parties, under assumptions about how they may communicate. These restrictions are expressed as constraints involving the eigenvalues of the density matrix of one of the parties. The thesis is divided into two parts.
\r\n\r\nPart I (Chapters 1-4) explores what is possible if the two parties may use only classical communication. A well-known result by M. Nielsen says that this is intimately connected to the mathematical notion of majorization. If entanglement catalysis is permitted, then the relevant notion is an extension of majorization known as the trumping relation. In Part I, we study the structure of the trumping relation.
\r\n\r\nPart II (Chapters 5-9) considers the question of how a state can change as a result of quantum communication between the parties; i.e., one party sends the other a portion of the jointly held quantum system. Given the spectrum of the initial state, it turns out that the possible spectra of the final state are given by the solutions to linear inequalities. We develop a method for deriving these inequalities, using a variational principle. In order to apply this principle, we need to know when certain subvarieties of a Grassmannian variety intersect, which can be regarded as a problem in Grassmannian cohomology. We discuss this cohomology and derive the conditions for nontrivial intersections. Finally, we illustrate how these intersections give rise to the desired inequalities.
", "doi": "10.7907/7097-1657", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:1519", "collection": "thesis", "collection_id": "1519", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-04272005-130936", "primary_object_url": { "basename": "Ozakin_ai_2004.pdf", "content": "final", "filesize": 5188309, "license": "other", "mime_type": "application/pdf", "url": "/1519/1/Ozakin_ai_2004.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "RG-Flows, AdS/CFT Correspondence and Stability of Non-Dilatonic Branes", "author": [ { "family_name": "Ozakin", "given_name": "Arkadas Inan", "clpid": "Ozakin-Arkadas-Inan" } ], "thesis_advisor": [ { "family_name": "Gubser", "given_name": "Steven Scott", "clpid": "Gubser-S-S" } ], "thesis_committee": [ { "family_name": "Gubser", "given_name": "Steven Scott", "clpid": "Gubser-S-S" }, { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "The possibility of having multiple renormalization group (RG) flows (one of which is supersymmetric) between two fixed points is investigated in the context of anti de Sitter / conformal field theory (AdS/CFT) correspondence. An analysis of a toy-model potential suggests that such flows are likely to exist. Superpotential methods are used in the context of finite temperature AdS/CFT to derive a black brane solution which approximates various finite temperature RG-flows in AdS/CFT near the horizon. This solution is also used in formulating a notion of univerality classes of instabilities of black braves. Instabilities of D3, M2 and M5-branes are investigated numerically, and the results confirm the predictions of the proposal of universality classes.", "doi": "10.7907/DQKG-HY63", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:1747", "collection": "thesis", "collection_id": "1747", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05122004-113132", "primary_object_url": { "basename": "jimh_thesis.pdf", "content": "final", "filesize": 1794965, "license": "other", "mime_type": "application/pdf", "url": "/1747/1/jimh_thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Analysis of Quantum Error-Correcting Codes: Symplectic Lattice Codes and Toric Codes", "author": [ { "family_name": "Harrington", "given_name": "James William", "clpid": "Harrington-James-William" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Politzer", "given_name": "Hugh David", "orcid": "0000-0002-4983-6621", "clpid": "Politzer-H-D" }, { "family_name": "Mabuchi", "given_name": "Hideo", "orcid": "0000-0002-5156-7678", "clpid": "Mabuchi-H" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Quantum information theory is concerned with identifying how quantum mechanical resources, such as entangled quantum states, can be utilized for a number of information processing tasks, including data storage, computation, communication, and cryptography. Efficient quantum algorithms and protocols have been developed for performing some tasks (e.g., factoring large numbers, securely communicating over a public channel, and simulating quantum mechanical systems) that appear to be very difficult with just classical resources. In addition to identifying the separation between classical and quantum computational power, much of the theoretical focus in this field over the last decade has been concerned with finding novel ways of encoding quantum information that are robust against errors, which is an important step toward building practical quantum information processing devices.\r\n\r\nIn this thesis I present some results on the quantum error-correcting properties of oscillator codes (also described as symplectic lattice codes) and toric codes. Any harmonic oscillator system, such as a mode of light, can be encoded with quantum information via symplectic lattice codes that are robust against shifts in the system's continuous quantum variables. I show the existence of lattice codes whose achievable rates match the one-shot coherent information over the Gaussian quantum channel. Also, I construct a family of symplectic self-dual lattices and search for optimal encodings of quantum information distributed between several oscillators.\r\n\r\nToric codes provide encodings of quantum information into two-dimensional spin lattices that are robust against local clusters of errors and which require only local quantum operations for error correction. Numerical simulations of this system under realistic error models provide a calculation of the accuracy threshold for quantum memory using toric codes, which can be related to phase transitions in particular condensed matter models. I also present a local classical processing scheme for correcting errors on toric codes, which demonstrates that quantum information can be maintained in two dimensions by purely local quantum and classical resources.", "doi": "10.7907/AHMQ-EG82", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:1873", "collection": "thesis", "collection_id": "1873", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05192004-164713", "primary_object_url": { "basename": "CSAthesisv4.pdf", "content": "final", "filesize": 870228, "license": "other", "mime_type": "application/pdf", "url": "/1873/1/CSAthesisv4.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Extending Quantum Error Correction: New Continuous Measurement Protocols and Improved Fault-Tolerant Overhead", "author": [ { "family_name": "Ahn", "given_name": "Charlene Sonja", "clpid": "Ahn-Charlene-Sonja" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Milburn", "given_name": "Gerard", "orcid": "0000-0002-5404-9681", "clpid": "Milburn-G" }, { "family_name": "Mabuchi", "given_name": "Hideo", "orcid": "0000-0002-5156-7678", "clpid": "Mabuchi-H" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Quantum mechanical applications range from quantum computers to quantum key distribution to teleportation. In these applications, quantum error correction is extremely important for protecting quantum states against decoherence. Here I present two main results regarding quantum error correction protocols.
\r\n\r\nThe first main topic I address is the development of continuous-time quantum error correction protocols via combination with techniques from quantum control. These protocols rely on weak measurement and Hamiltonian feedback instead of the projective measurements and unitary gates usually assumed by canonical quantum error correction. I show that a subclass of these protocols can be understood as a quantum feedback protocol, and analytically analyze the general case using the stabilizer formalism; I show that in this case perfect feedback can perfectly protect a stabilizer subspace. I also show through numerical simulations that another subclass of these protocols does better than canonical quantum error correction when the time between corrections is limited.
\r\n\r\nThe second main topic is development of improved overhead results for fault-tolerant computation. In particular, through analysis of topological quantum error correcting codes, it will be shown that the required blowup in depth of a noisy circuit performing a fault-tolerant computation can be reduced to a factor of O(log log L), an improvement over previous results. Showing this requires investigation into a local method of performing fault-tolerant correction on a topological code of arbitrary dimension.
", "doi": "10.7907/THD5-A335", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:2139", "collection": "thesis", "collection_id": "2139", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05272004-174253", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 917993, "license": "other", "mime_type": "application/pdf", "url": "/2139/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Investigations in Quantum Computing: Causality and Graph Isomorphism", "author": [ { "family_name": "Beckman", "given_name": "David Eugene", "clpid": "Beckman-David-Eugene" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Politzer", "given_name": "Hugh David", "orcid": "0000-0002-4983-6621", "clpid": "Politzer-H-D" }, { "family_name": "Mabuchi", "given_name": "Hideo", "orcid": "0000-0002-5156-7678", "clpid": "Mabuchi-H" }, { "family_name": "Frautschi", "given_name": "Steven C.", "clpid": "Frautschi-S-C" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "In this thesis I explore two different types of limits on the time complexity of quantum computation---that is, limits on how much time is required to perform a given class of quantum operations on a quantum system. Upper limits can be found by explicit construction; I explore this approach for the problem of determining whether two graphs are isomorphic. Finding lower limits, on the other hand, usually requires appeal to some fundamental principle of the operation under consideration; I use this approach to derive lower limits placed by the requirements of relativistic causality on the time required for implementation of some nonlocal quantum operations. In some situations these limits are attainable, but for other physical spacetime geometries we exhibit classes of operations which do not violate relativistic causality but which are nevertheless not implementable.", "doi": "10.7907/S1R0-0V87", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:649", "collection": "thesis", "collection_id": "649", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-02172004-173217", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 1237900, "license": "other", "mime_type": "application/pdf", "url": "/649/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Quantum Information Theory: Classical Communication Over Quantum Channels", "author": [ { "family_name": "Cortese", "given_name": "John Anthony", "clpid": "Cortese-John-Anthony" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Mabuchi", "given_name": "Hideo", "orcid": "0000-0002-5156-7678", "clpid": "Mabuchi-H" }, { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" }, { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis studies classical communication over quantum channels. Chapter 1 describes an algebraic technique which extends several previously known qubit channel capacity results to the qudit quantum channel case. Chapter 2 derives a formula for the relative entropy function of two qubit density matrices in terms of their Bloch vectors. The application of the Bloch vector relative entropy formula to the determination of Holevo-Schumacher-Westmoreland (HSW) capacities for qubit quantum channels is discussed. Chapter 3 outlines several numerical simulation results which support theoretical conclusions and conjectures discussed in Chapters 1 and 2. Chapter 4 closes the thesis with comments, examples and discussion on the additivity of Holevo Chi and the HSW channel capacity.", "doi": "10.7907/V68W-YK95", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:1300", "collection": "thesis", "collection_id": "1300", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-04082003-111058", "primary_object_url": { "basename": "99thesis_whole.pdf", "content": "final", "filesize": 5161352, "license": "other", "mime_type": "application/pdf", "url": "/1300/12/99thesis_whole.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Measurement and Control of Individual Quanta in Cavity QED", "author": [ { "family_name": "Lynn", "given_name": "Theresa Wan-Zhen", "clpid": "Lynn-Theresa-Wan-Zhen" } ], "thesis_advisor": [ { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" } ], "thesis_committee": [ { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" }, { "family_name": "Hughes", "given_name": "Emlyn Willard", "orcid": "0000-0002-5381-4759", "clpid": "Hughes-Emlyn-Willard" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Roukes", "given_name": "Michael Lee", "orcid": "0000-0002-2916-6026", "clpid": "Roukes-M-L" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Cavity quantum electrodynamics (QED) in the strong-coupling regime provides the opportunity to monitor and control the dynamics of a simple quantum system. A single Cesium atom interacts strongly with single-photon fields in the mode of a high-finesse optical cavity. When the resulting coherent coupling rate dominates dissipation in the system, strong coupling is realized and the system displays distinctively quantum behavior. The coupling between atomic internal states and the quantized cavity field allows for diverse protocols in quantum state preparation, quantum communication, and quantum logic. However, the atom's external or motional state must also be taken into account. My research develops cavity QED in the limit where the coherent atom-field coupling dominates the atomic kinetic energy and thus significantly affects the atomic center-of-mass motion. In this regime, the interaction of the atom with the cavity field provides both a means of controlling atomic motion and a signal for detecting that motion in real time with high signal-to-noise. The sensing capability of the ``atom-cavity microscope\" is exploited to trap single atoms with single-photon fields and to monitor their orbits in real time as they are bound in the cavity. Such real-time position sensing is the basis for a detailed strategy and ongoing experiment to actively stabilize select aspects of an atom's motion within the cavity. As the cavity-enabled position measurement approaches the standard quantum limit, this work begins to realize a quantum servo for atomic position and to address questions of optimal state estimation and state preparation. In combination with other progress in cavity QED, it furthers the goal of controlled atom-field interactions for quantum information science.", "doi": "10.7907/PSPJ-6H44", "publication_date": "2003", "thesis_type": "phd", "thesis_year": "2003" }, { "id": "thesis:2240", "collection": "thesis", "collection_id": "2240", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05292003-214249", "primary_object_url": { "basename": "Buck_2003.pdf", "content": "final", "filesize": 2663647, "license": "other", "mime_type": "application/pdf", "url": "/2240/1/Buck_2003.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Cavity QED in Microsphere and Fabry-Perot Cavities", "author": [ { "family_name": "Buck", "given_name": "Joseph Robert", "clpid": "Buck-Joseph- Robert" } ], "thesis_advisor": [ { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" } ], "thesis_committee": [ { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" }, { "family_name": "Peck", "given_name": "Charles W.", "clpid": "Peck-C-W" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Libbrecht", "given_name": "Kenneth George", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "A long-standing ambition in the field of cavity quantum electrodynamics has been to trap single atoms inside high-Q cavities in a regime of strong coupling. Our goal has been to develop techniques for trapping that are compatible with strong coupling and that do not interfere with the cavity QED interactions. This is crucial for applications to quantum computation and communication. We have accomplished this goal by creating a trapping potential through an intracavity FORT at the 'magic' wavelength for Cesium, 935.6 nm. Unlike typical FORTs, where the signs of the AC-Stark shifts for excited and ground states are opposite, our trap causes small shifts to the relevant transition frequencies, enabling a trapping potential for the center-of-mass motion that is largely independent of the internal atomic state. This has enabled us to achieve extended trapping times (3 sec) for individual Cesium atoms in cavity QED in a regime of strong coupling. Although our longest lifetimes are obtained when the probing fields are turned off, the atoms can also be continuously monitored, leading to mean trapping times of 0.4 sec, with some atoms observed for over 1 sec.
\r\n\r\nAn important tool for studying atom-field interactions is a high-Q cavity with small mode volume. Considerable effort has been made in advancing our capabilities for high-Q resonators. While much of our work involves Fabry-Perot cavities, some of the highest quality optical resonators to date have been achieved with the whispering gallery modes (WGMs) of quartz microspheres (Q = 8 x 10\u2079). Therefore, considerable effort has been given to understanding the usefulness of microspheres for cavity QED with strong coupling. We have also worked at manufacturing high-Q microspheres suitable for cavity QED. To this end, we have been successful at making spheres with a radius of 10 microns and Q = 10\u2077.
", "doi": "10.7907/585P-6F46", "publication_date": "2003", "thesis_type": "phd", "thesis_year": "2003" }, { "id": "thesis:2652", "collection": "thesis", "collection_id": "2652", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06202002-170522", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 571645, "license": "other", "mime_type": "application/pdf", "url": "/2652/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Graph-Based Codes and Iterative Decoding", "author": [ { "family_name": "Khandekar", "given_name": "Aamod Dinkar", "clpid": "Khandekar-Aamod-Dinkar" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Bruck", "given_name": "Jehoshua", "orcid": "0000-0001-8474-0812", "clpid": "Bruck-J" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The field of error correcting codes was revolutionized by the introduction of turbo codes in 1993. These codes demonstrated dramatic performance improvements over any previously known codes, with significantly lower complexity. Since then, much progress has been made towards understanding the performance of these codes, as well as in using this understanding to design even better codes.
\r\n\r\nThis thesis takes a few more steps in both these directions. We develop a new technique, called the typical set bound, for analyzing the asymptotic performance of code ensembles based on their weight enumerators. This technique yields very tight bounds on the maximum-likelihood decoding threshold of code ensembles, and is powerful enough to reproduce Shannon's noisy coding theorem for the class of binary-input symmetric channels.
\r\n\r\nWe also introduce a new class of codes called irregular repeat-accumulate (IRA) codes, which are adapted from the previously known class of repeat-accumulate (RA) codes. These codes are competitive in terms of decoding performance with the class of irregular low-density parity-check (LDPC) codes, which are arguably the best class of codes known today, at least for long block lengths. In addition, IRA codes have a significant advantage over irregular LDPC codes in terms of encoding complexity.
\r\n\r\nWe also derive an analytical bound regarding iterative decoding thresholds of code ensembles on general binary-input symmetric channels, an area in which theoretical results are currently lacking.
", "doi": "10.7907/Q06G-MW38", "publication_date": "2003", "thesis_type": "phd", "thesis_year": "2003" }, { "id": "thesis:1937", "collection": "thesis", "collection_id": "1937", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05222003-121058", "primary_object_url": { "basename": "main.pdf", "content": "final", "filesize": 836909, "license": "other", "mime_type": "application/pdf", "url": "/1937/1/main.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Characterizing Entanglement in Quantum Information", "author": [ { "family_name": "Spedalieri", "given_name": "Federico Maximiliano", "clpid": "Spedalieri-Federico-Maximiliano" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Schumacher", "given_name": "Benjamin", "clpid": "Schumacher-B" }, { "family_name": "Peck", "given_name": "Charles W.", "clpid": "Peck-C-W" }, { "family_name": "Mabuchi", "given_name": "Hideo", "orcid": "0000-0002-5156-7678", "clpid": "Mabuchi-H" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Entanglement is a key resource in the emerging field of Quantum Information. The strong correlations between systems described by an entangled state allow us to perform certain tasks more efficiently than it would be possible by using only classical resources. This is why the characterization of entanglement is one of the most important problems in Quantum Information.
\r\n\r\nIn this thesis, we analyze several aspects of entanglement. First, we introduce a new family of criteria to determine if a bipartite mixed state is entangled or not. This family consists of a sequence of tests that can be implemented efficiently, and has the property that all entangled states can be detected by some test in the sequence.
\r\n\r\nEach test in the family can be stated as a semidefinite program, which is a class of convex optimization problems. The duality structure of these programs allows us to explicitly construct an entanglement witness that proves entanglement of a state, whenever the state fails one of the tests in the sequence. The entanglement witnesses constructed in this manner have well-defined algebraic properties that can be used to give a characterization of the interior of the set of all possible entanglement witnesses, as well as the set of strictly positive bihermitian forms and the set of strictly positive maps.
\r\n\r\nWe also study deterministic transformations of three-qubit pure state when only local operations and classical communication (LOCC) are allowed. We derive strong constraints that the operations and states involved must satisfy, and we apply these results to characterize the set of real states that can be obtained from the GHZ state by LOCC.
", "doi": "10.7907/KFMV-E833", "publication_date": "2003", "thesis_type": "phd", "thesis_year": "2003" }, { "id": "thesis:2285", "collection": "thesis", "collection_id": "2285", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05302002-130637", "primary_object_url": { "basename": "phd2002.pdf", "content": "final", "filesize": 642995, "license": "other", "mime_type": "application/pdf", "url": "/2285/1/phd2002.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Aspects of Non-Fermi-Liquid Metals", "author": [ { "family_name": "Pivovarov", "given_name": "Evgueny (Eugene)", "clpid": "Pivovarov-Evgueny-Eugene" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Nayak", "given_name": "Chetan", "clpid": "Nayak-C" }, { "family_name": "Cross", "given_name": "Michael Clifford", "clpid": "Cross-M-C" }, { "family_name": "Yeh", "given_name": "Nai-Chang", "orcid": "0000-0002-1826-419X", "clpid": "Yeh-Nai-Chang" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "We consider several examples of metallic systems that exhibit non-Fermi-liquid behavior. In these examples the system is not a Fermi liquid due to the presence of a \"hidden\" order. The primary models are density waves with an odd-frequency-dependent order parameter and density waves with d-wave symmetry. In the first model, the same-time correlation functions vanish and there is a conventional Fermi surface. In the second model, the gap vanishes at the nodes. We derive the phase diagrams and study the thermodynamic and kinetic properties. We also consider the effects of competing orders on the phase diagram when the underlying microscopic interaction has a high symmetry.", "doi": "10.7907/20WA-FT36", "publication_date": "2002", "thesis_type": "phd", "thesis_year": "2002" }, { "id": "thesis:6851", "collection": "thesis", "collection_id": "6851", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:03142012-093815562", "type": "thesis", "title": "Controlling Quantum Information", "author": [ { "family_name": "Landahl", "given_name": "Andrew John", "clpid": "Landahl-Andrew-John" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" }, { "family_name": "Mabuchi", "given_name": "Hideo", "clpid": "Mabuchi-H" }, { "family_name": "Thorne", "given_name": "Kip S.", "clpid": "Thorne-K-S" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Quantum information science explores ways in which quantum physical laws can be harnessed to control the acquisition, transmission, protection, and processing\r\nof information. This field has seen explosive growth in the past several years from progress on both theoretical and experimental fronts. Essential to this endeavor are methods for controlling quantum information.
\r\n\r\nIn this thesis, I present three new approaches for controlling quantum information. First, I present a new protocol for continuously protecting unknown quantum\r\nstates from noise. This protocol combines and expands ideas from the theories of quantum error correction and quantum feedback control. The result can outperform either approach by itself. I generalize this protocol to all known quantum\r\nstabilizer codes, and study its application to the three-qubit repetition code in detail via Monte Carlo simulations.
\r\n\r\nNext, I present several new protocols for controlling quantum information that are fault-tolerant. These protocols require only local quantum processing due to\r\nthe topological properties of the quantum error correcting codes upon which they are built. I show that each protocol's fault-dependence behavior exhibits an order-disorder phase transition when mapped onto an associated statistical-mechanical model. I review the critical error rates of these protocols found by numerical study\r\nof the associated models, and I present new analytic bounds for them using a self-avoiding random walk argument. Moreover, I discuss fault-tolerant procedures for encoding, error-correction, computing, and decoding quantum information using these protocols, and calculate the accuracy threshold of fault-tolerant quantum memory for protocols using them.
\r\n\r\nI end by presenting a new class of quantum algorithms that solve combinatorial optimization problems solely by measurement. I compute the running times of\r\nthese algorithms by establishing an explicit dynamical model for the measurement process. This model, the digitized version of von Neumann's measurement model,\r\nis recognized as Kitaev's phase estimation algorithm. I show that the running times of these algorithms are closely related to the running times of adiabatic quantum algorithms. Finally, I present a two-measurement algorithm that achieves a quadratic speedup for Grover's unstructured search problem.
", "doi": "10.7907/BJ0Q-C297", "publication_date": "2002", "thesis_type": "phd", "thesis_year": "2002" }, { "id": "thesis:6769", "collection": "thesis", "collection_id": "6769", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01202012-104927686", "primary_object_url": { "basename": "Gingrich_rm_2002.pdf", "content": "final", "filesize": 17319492, "license": "other", "mime_type": "application/pdf", "url": "/6769/1/Gingrich_rm_2002.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Entanglement of Multipartite Quantum States and the Generalized Quantum Search", "author": [ { "family_name": "Gingrich", "given_name": "Robert Michael", "clpid": "Gingrich-Robert-Michael" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Adami", "given_name": "Christoph Carl", "clpid": "Adami-C-C" }, { "family_name": "Frautschi", "given_name": "Steven C.", "clpid": "Frautschi-S-C" }, { "family_name": "Mabuchi", "given_name": "Hideo", "clpid": "Mabuchi-H" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "In chapter 2 various parameterizations for the orbits under local unitary transformations of three-qubit pure states are analyzed. It is shown that the entanglement monotones of any multipartite pure state uniquely determine the orbit of that state. It follows that there must be an entanglement monotone for three-qubit pure states which depends on the Kempe invariant defined in [1]. A form for such an entanglement monotone is proposed. A theorem is proved that significantly reduces the number of entanglement monotones that must be looked at to find the maximal probability of transforming one multipartite state\r\nto another.
\r\n\r\nIn chapter 3 Grover's unstructured quantum search algorithm is generalized to use an arbitrary starting superposition and an arbitrary unitary matrix. A formula for the probability of the generalized Grover's algorithm succeeding after n iterations is derived. This formula is used to determine the optimal strategy for using the unstructured quantum search algorithm. The speedup obtained illustrates that a hybrid use of quantum computing and classical computing techniques can yield a performance that is better than either alone. The analysis is extended to the case of a society of k quantum searches acting in parallel.
\r\n\r\nIn chapter 4 the positive map \u0413 : p \u2192 (Tr\u03c1) - \u03c1 is introduced as a separability criterion. Any separable state is mapped by the tensor product of \u0413 and the identity in to a non-negative operator, which provides a necessary condition for separability. If \u0413 acts on a two-dimensional subsystem, then it is equivalent to partial transposition and therefore also sufficient for 2 x 2 and 2 x 3 systems. Finally, a connection between this map for two qubits and complex conjugation in the \"magic\" basis [2] is displayed.
", "doi": "10.7907/0M1P-NS54", "publication_date": "2002", "thesis_type": "phd", "thesis_year": "2002" }, { "id": "thesis:5959", "collection": "thesis", "collection_id": "5959", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06242010-150733171", "type": "thesis", "title": "Brane Models and the Hierarchy Problem", "author": [ { "family_name": "Goldberger", "given_name": "Walter D.", "clpid": "Goldberger-Walter-D" } ], "thesis_advisor": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" } ], "thesis_committee": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Porter", "given_name": "Frank C.", "orcid": "0000-0003-1948-8889", "clpid": "Porter-F-C" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "It has been recently proposed that higher-dimensional field theory models in the presence of extended defects (\"branes\") may play a role in addressing the gauge hierarchy problem. In this thesis we consider several aspects of such field theories. First we perform the Kaluza-Klein reduction of a bulk scalar field propagating in the scenario of Randall and Sundrum, which consists of a region of five-dimensional anti-deSitter space bounded by two three-branes. We then propose a simple mechanism, based on the dynamics of a bulk scalar field, for stabilizing the modulus field (the \"radion\") corresponding to the size of the compact dimension in the Randall-Sundrum scenario. Some implications of this stabilization mechanism for low-energy phenomenology are described. Next, we investigate the one-loop quantum corrections to the radion effective potential. We show that for large brane separation, the quantum effects are power suppressed and therefore have a negligible effect on the bulk dynamics once a classical stabilization mechanism is in place. Finally, we study the ultraviolet divergence structure of field theory in the presence of branes and find that brane-localized divergences arise both at the classical and quantum level. We show how to interpret the classical divergences by the usual regularization and renormalization procedure of quantum field theory.", "doi": "10.7907/zmfm-yd07", "publication_date": "2001", "thesis_type": "phd", "thesis_year": "2001" }, { "id": "thesis:4867", "collection": "thesis", "collection_id": "4867", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12082006-104418", "primary_object_url": { "basename": "Popescu_c_2001.pdf", "content": "final", "filesize": 5985964, "license": "other", "mime_type": "application/pdf", "url": "/4867/1/Popescu_c_2001.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Branes, Brane Actions and Applications to Field Theory", "author": [ { "family_name": "Popescu", "given_name": "Costin Radu", "clpid": "Popescu-Costin-Radu" } ], "thesis_advisor": [ { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" } ], "thesis_committee": [ { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" }, { "family_name": "Politzer", "given_name": "Hugh David", "orcid": "0000-0002-4983-6621", "clpid": "Politzer-H-D" }, { "family_name": "Porter", "given_name": "Frank C.", "orcid": "0000-0003-1948-8889", "clpid": "Porter-F-C" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "This thesis describes the construction of supersymmetric world-volume actions for various kinds of extended objects that appear in string theory, the so-called p-branes, D-branes and M-branes. We also present an application of branes to computing the spectrum of a conformal field theory in the context of the AdS-CFT correspondence.\r\n", "doi": "10.7907/qr6g-tp18", "publication_date": "2001", "thesis_type": "phd", "thesis_year": "2001" }, { "id": "thesis:3688", "collection": "thesis", "collection_id": "3688", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-09222005-105541", "primary_object_url": { "basename": "Hood_cj_2000.pdf", "content": "final", "filesize": 12380220, "license": "other", "mime_type": "application/pdf", "url": "/3688/1/Hood_cj_2000.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Real-Time Measurement and Trapping of Single Atoms by Single Photons", "author": [ { "family_name": "Hood", "given_name": "Christina J.", "clpid": "Hood-Christina-J" } ], "thesis_advisor": [ { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" }, { "family_name": "Porter", "given_name": "Frank C.", "orcid": "0000-0003-1948-8889", "clpid": "Porter-F-C" } ], "thesis_committee": [ { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" }, { "family_name": "Eisenstein", "given_name": "James P.", "orcid": "0000-0001-5460-0464", "clpid": "Eisenstein-J-P" }, { "family_name": "Libbrecht", "given_name": "Kenneth George", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Cavity quantum electrodynamics (QED), the system of a single atom interacting with a single mode of a high finesse optical resonator, has tremendous potential for use in quantum logic, quantum information processing, and in enabling observation of quantum mechanical effects in the laboratory. The work of this thesis demonstrates a number of steps toward realizing these goals, by employing an experimental system with the strongest atom-field coupling achieved to date in optical cavity QED. The effects of strong coupling in cavity QED are studied for single cold atoms measured one at a time, in real time. The passage of single atoms through the cavity is employed to map out the frequency response of the system, and to demonstrate that quantum rather than semiclassical theory provides the correct theoretical model. The mechanical effects of strong coupling on single atoms are explored, these experiments demonstrating the first trapping of single atoms with single photons. Additionally, strong coupling enables high signal-to-noise ratio for monitoring atomic position at single photon field strengths; this capability is employed to investigate the motion of atoms trapped within the cavity. The transmitted cavity field is used to reconstruct the trajectories of single atoms, thereby realizing a new form of microscopy - the Atom-Cavity Microscope. Technical developments necessary to create the cavities used in this experiment are detailed. Ideas for future extensions to the experiment are proposed; a zero light-shift dipole force trap, and measurement of photon statistics of a single strongly coupled atom (which realizes a photon blockade device) are discussed.", "doi": "10.7907/41KH-2T46", "publication_date": "2000", "thesis_type": "phd", "thesis_year": "2000" }, { "id": "thesis:17556", "collection": "thesis", "collection_id": "17556", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:07252025-144149295", "primary_object_url": { "basename": "Bliss_JL_1999.pdf", "content": "final", "filesize": 23386522, "license": "other", "mime_type": "application/pdf", "url": "/17556/1/Bliss_JL_1999.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Collisional Studies of Ultracold Cesium", "author": [ { "family_name": "Bliss", "given_name": "Joshua Lovis", "clpid": "Bliss-Joshua-Lovis" } ], "thesis_advisor": [ { "family_name": "Libbrecht", "given_name": "Kenneth George", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "thesis_committee": [ { "family_name": "Libbrecht", "given_name": "Kenneth George", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" }, { "family_name": "Eisenstein", "given_name": "James P.", "orcid": "0000-0001-5460-0464", "clpid": "Eisenstein-J-P" }, { "family_name": "Zmuidzinas", "given_name": "Jonas", "orcid": "0000-0002-3330-5439", "clpid": "Zmuidzinas-J" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Spin-polarized neutral cesium atoms are confined in a magnetostatic trap in a cryogenic\r\napparatus. The atoms are prepared in the F = 4, mF = 4 state and cooled,\r\nwith rf-assisted evaporative cooling, to less than 10 microKelvin.
\r\n\r\nThe elastic scattering cross section is measured by disequilibrating magnetostatically\r\ntrapped atoms and observing the rate of equilibration. A computer simulation is\r\npresented, the results of which are used to extract the elastic scattering cross section\r\nfrom the measured rates of equilibration. For cesium atoms in the F = 4, mF = 4\r\nstate, the elastic cross section is confirmed to have a resonant magnitude which varies\r\ninversely with the mean kinetic energy, implying a scattering resonance.
\r\n\r\nA design for a new beam source of cold neutral atoms, based on an optical funnel\r\nwith a pyramid mirror configuration, is also presented.
", "doi": "10.7907/fcz4-pd11", "publication_date": "1999", "thesis_type": "phd", "thesis_year": "1999" }, { "id": "thesis:17661", "collection": "thesis", "collection_id": "17661", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09022025-221121899", "primary_object_url": { "basename": "Chadha_M_1998.pdf", "content": "final", "filesize": 68791616, "license": "other", "mime_type": "application/pdf", "url": "/17661/1/Chadha_M_1998.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "A Measurement of the Michel Parameters \u03c1 and \u019e in Leptonic Tau Decays", "author": [ { "family_name": "Chadha", "given_name": "Mandeepa", "clpid": "Chadha-Mandeepa" } ], "thesis_advisor": [ { "family_name": "Barish", "given_name": "Barry C.", "orcid": "0000-0001-6386-7371", "clpid": "Barish-B-C" } ], "thesis_committee": [ { "family_name": "Barish", "given_name": "Barry C.", "orcid": "0000-0001-6386-7371", "clpid": "Barish-B-C" }, { "family_name": "Hughes", "given_name": "Emlyn Willard", "orcid": "0000-0002-5381-4759", "clpid": "Hughes-Emlyn-Willard" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Weinstein", "given_name": "Alan Jay", "orcid": "0000-0002-0928-6784", "clpid": "Weinstein-Alan-J-Physics" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis describes a precise measurement of the Michel parameters \u03c1 and \u019e using\r\nthe leptonic tau decays recorded by the CLEO II detector. These measurements can\r\nbe used to provide limits on the non-(V - A) contributions to the Lorentz structure\r\nof the charged weak interactions in tau decays.
\r\n\r\nThe electronic decay of the tau lepton, \u03c4 \u2192 evv, is used to measure the spectral\r\nshape Michel parameter:
\r\n\r\n\u03c1\u03b5 = 0.732 \u00b1 0.014 \u00b1 0.009,
\r\n\r\nwhere the first error is statistical and the second systematic. This measurement is\r\nextracted from the electron energy spectrum; the energy spectrum is insensitive to the\r\nlow energy spectral shape Michel parameter \u019e\u03b5, and thus insensitive to the presence\r\nof scalar couplings.
\r\n\r\nThe muonic decay mode of the tau lepton, \u03c4 \u2192 \u00b5vv, is used to measure both the\r\nspectral shape Michel parameters:
\r\n\r\n\u03c1\u00b5 = 0.747 \u00b1 0.048 \u00b1 0.044
\r\n\r\nand \u019e\u00b5 = 0.010 \u00b1 0.149 \u00b1 0.171
\r\n\r\nsimultaneously. Once again, the first errors are statistical and the second systematic.\r\nThe two parameters are strongly correlated; the correlation coefficient C\u03c1\u019e is 0.949.
\r\n\r\nAssuming lepton universality of the vector-like couplings, the two leptonic decay\r\nmodes are simultaneously analyzed to improve the measurement of the \u019e parameter.\r\nSince the electron mode is insensitive to the \u019e parameter, we can measure \u03c1 very\r\nprecisely using the electron mode. This measurement can now be used to constrain
\r\n\r\nthe \u03c1 measurement in the muon analysis, and thus obtain:
\r\n\r\n\u03c1\u03b5\u00b5 = 0.735 \u00b1 0.013 \u00b1 0.008
\r\n\r\nand \u019e\u03b5\u00b5 = -0.015 \u00b1 0.061 \u00b1 0.062,
\r\n\r\nwhere the first errors a.re statistical and the second systematic. The correlation coefficient\r\nis now reduced to 0.615.
\r\n\r\nThese measurements are all more precise than previous measuren1ents; some are\r\nmore precise than previous world average measurements. No indications for any\r\ndeviations from the Minimal Standard Model have been found.
\r\n\r\nThis measurement of the \u019e parameter provides a lower limit on the charged Higgs\r\nmass in the Minimal Supersymmetric Standard Model: mH\u00b1 > (0.97 x tan \u03b2) GeV\r\nat the 90% confidence level. This limit is not very interesting unless tan \u03b2 is very\r\nlarge.
", "doi": "10.7907/xkhh-jq80", "publication_date": "1998", "thesis_type": "phd", "thesis_year": "1998" }, { "id": "thesis:2900", "collection": "thesis", "collection_id": "2900", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-07162004-113028", "primary_object_url": { "basename": "THESIS.pdf", "content": "updated", "filesize": 564205, "license": "other", "mime_type": "application/pdf", "url": "/2900/2/THESIS.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Stabilizer Codes and Quantum Error Correction", "author": [ { "family_name": "Gottesman", "given_name": "Daniel Eric", "clpid": "Gottesman-Daniel-Eric" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" }, { "family_name": "Koonin", "given_name": "Steven E.", "orcid": "0000-0001-5897-5319", "clpid": "Koonin-S-E" }, { "family_name": "Prince", "given_name": "Thomas A.", "orcid": "0000-0002-8850-3627", "clpid": "Prince-T-A" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed to meet this challenge. A group-theoretical structure and associated subclass of quantum codes, the stabilizer codes, has proved particularly fruitful in producing codes and in understanding the structure of both specific codes and classes of codes. I will give an overview of the field of quantum error correction and the formalism of stabilizer codes. In the context of stabilizer codes, I will discuss a number of known codes, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation", "doi": "10.7907/rzr7-dt72", "publication_date": "1997", "thesis_type": "phd", "thesis_year": "1997" }, { "id": "thesis:13579", "collection": "thesis", "collection_id": "13579", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:11192019-171459529", "primary_object_url": { "basename": "bradford-kb-1997.pdf", "content": "final", "filesize": 3064818, "license": "other", "mime_type": "application/pdf", "url": "/13579/1/bradford-kb-1997.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Aspects of Non-Abelian Many Body Physics", "author": [ { "family_name": "Bradford", "given_name": "Kent B.", "clpid": "Bradford-Kent-B" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Politzer", "given_name": "Hugh David", "orcid": "0000-0002-4983-6621", "clpid": "Politzer-H-D" }, { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Weichman", "given_name": "Peter B.", "clpid": "Weichman-Peter-B" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "The general formulation of quantum statistical mechanics hints at interesting generalizations of the usual Bose/Fermi framework in two spatial dimensions. Anyon statistics, which is essentially a continuous interpolation between Bose and Fermi statistics, is relevant to the Fractional Quantum Hall Effect in two-dimensional (i.e., thin layer) condensed matter systems. In addition, the possibility of non-abelian statistics, in which the multi-particle wavefunction transforms as a representation of a non-abelian group under the exchange of indistinguishable particles, has been explored. Spontaneously broken non-abelian gauge theories in (2 + 1) dimensions often have stable topological defects, called non-abelian vortices, that experience non-abelian statistics. In addition, it has been suggested that degenerate quasihole multiplets in Quantum Hall systems also transform as non-abelian representations of the braid group under particle exchange. In this thesis, I explore the braiding properties of systems of two-cycle flux vortices in a residual S\u2083 discrete gauge group. The individual vortices are uncharged, but multi-vortex states can have Cheshire charge. The uncharged sectors all have non-vanishing bosonic subspaces, as do the non-abelian charged trivial flux sectors. A kinetic Hamiltonian for vortices on a periodic lattice is constructed. There is a modification to the translational symmetry in the periodically identified direction for non-trivial Z\u2082 charged sectors. The ground state energies for various three and four vortex sectors is numerically determined. Typically, the ground state is bosonic, with a gap separating it from a non-abelian subspace.
", "doi": "10.7907/rn7x-3882", "publication_date": "1997", "thesis_type": "phd", "thesis_year": "1997" }, { "id": "thesis:3584", "collection": "thesis", "collection_id": "3584", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-09172007-144702", "primary_object_url": { "basename": "Chow_ck_1995.pdf", "content": "final", "filesize": 3378435, "license": "other", "mime_type": "application/pdf", "url": "/3584/1/Chow_ck_1995.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Heavy hadrons in the large Nc limit", "author": [ { "family_name": "Chow", "given_name": "Chi-Keung", "clpid": "Chow-C" } ], "thesis_advisor": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" } ], "thesis_committee": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Politzer", "given_name": "Hugh David", "orcid": "0000-0002-4983-6621", "clpid": "Politzer-H-D" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Frautschi", "given_name": "Steven C.", "clpid": "Frautschi-S-C" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.\r\n\r\nIn the heavy quark and large [...] limit, heavy baryons can be identified as bound states of heavy mesons and light baryons. The binding potential can be calculated under chiral perturbation theory, and is simple harmonic when [...]. The spectra and properties of these bound states agree reasonably well with the observed heavy baryons. In this framework, some non-perturbative quantities, like the orbital excitation energy and the slope of the Isgur-Wise form factor, can be evaluated. Moreover, the same universal Isgur-Wise form factor describes the semileptonic decays [...] and [...]. The formalism can also be used to study the spectra, stabilities and decay modes of exotic multiquark states.", "doi": "10.7907/7qz6-sg17", "publication_date": "1995", "thesis_type": "phd", "thesis_year": "1995" }, { "id": "thesis:3475", "collection": "thesis", "collection_id": "3475", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-09112008-135620", "primary_object_url": { "basename": "Yi_p_1994.pdf", "content": "final", "filesize": 4241220, "license": "other", "mime_type": "application/pdf", "url": "/3475/1/Yi_p_1994.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "On quantum fluctuations and black holes", "author": [ { "family_name": "Yi", "given_name": "Piljin", "clpid": "Yi-Piljin" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" }, { "family_name": "Trivedi", "given_name": "Sandip P.", "clpid": "Trivedi-S-P" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "We explore some exotic phenomena in charged black holes, arising from the second quantization of matter fields or from the first quantization of fundamental strings. Spherically symmetric magnetic black holes admit special modes of electrically charged fermions, known as Callan-Rubakov modes, which can be quantized efficiently. We find that the chargeless sector generates non-thermal quantum radiations from extremal Reissner-NordstrOm black holes, thereby reducing the black hole masses below the familiar classical bound in spite of the vanishing Hawking temperature. On the other hand, the charged sector induces a vacuum energy distribution and the gravitational backreaction thereof, which are particularly pronounced for extremal dilatonic black holes. Implications of these quantum effects are studied in great detail. Also considered is a string-inspired two-dimensional gravity with non-singular charged black holes among its solutions. After a lengthy discussion on the stability of these novel space-times, we speculate on the possibility and implications of nonsingular black holes in full-blown string theories.\r\n", "doi": "10.7907/8jtc-0d19", "publication_date": "1994", "thesis_type": "phd", "thesis_year": "1994" }, { "id": "thesis:7649", "collection": "thesis", "collection_id": "7649", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05012013-113552586", "primary_object_url": { "basename": "Apostolakis-j-1994.pdf", "content": "final", "filesize": 31124203, "license": "other", "mime_type": "application/pdf", "url": "/7649/1/Apostolakis-j-1994.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers", "author": [ { "family_name": "Apostolakis", "given_name": "John", "clpid": "Apostolakis-J" } ], "thesis_advisor": [ { "family_name": "Fox", "given_name": "Geoffrey C.", "clpid": "Fox-G-C" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Frautschi", "given_name": "Steven C.", "clpid": "Frautschi-S-C" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings \u03b2 up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L \u2264 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at \u03b2 = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/\u039b^\u2500_(Ms) = 3.52(6) at this \u03b2 and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced\r\nsignificantly for this local algorithm that is vectorizable and parallelizable.
\r\n\r\nWe also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional\r\nIsing spin model.
\r\n\r\nFinally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete \u03b2-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling \u03b2_E to effectively resum the series. For the latter case we see agreement for m/ \u039b^\u2500_(Ms) at , \u03b2 = 2.14, 2.26, 2.38 and 2.50. To three loops m/\u039b^\u2500_(Ms) = 3.047(35) at \u03b2 = 2.50, which is very close to the exact value m/ \u039b^\u2500_(Ms) = 2.943. Our last point at \u03b2 = 2.62 disagrees with this estimate however.
\r\n", "doi": "10.7907/be1d-0t13", "publication_date": "1994", "thesis_type": "phd", "thesis_year": "1994" }, { "id": "thesis:2577", "collection": "thesis", "collection_id": "2577", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06132007-131249", "primary_object_url": { "basename": "Bucher_m_1991.pdf", "content": "final", "filesize": 3257577, "license": "other", "mime_type": "application/pdf", "url": "/2577/1/Bucher_m_1991.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "On the Theory of Non-Abelian Vortices and Cosmic Strings", "author": [ { "family_name": "Bucher", "given_name": "Martin", "clpid": "Bucher-Martin" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Barish", "given_name": "Barry C.", "orcid": "0000-0001-6386-7371", "clpid": "Barish-B-C" }, { "family_name": "Politzer", "given_name": "Hugh David", "orcid": "0000-0002-4983-6621", "clpid": "Politzer-H-D" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "The thesis deals with the theory of non-Abelian vortices in two spatial dimensions and cosmic strings in three spatial dimensions that arise when a non-Abelian gauge symmetry G is broken to a non-Abelian unbroken symmetry group H by the condensation of a Higgs field. The first part of the thesis discusses the case in which H is discrete. In this case all of the gauge bosons acquire a large mass; however, at low energies discretely charged particles experience non-Abelian Aharonov-Bohm scattering off vortices, which can be used to measure the flux of the vortices. Vortices also experience non-Abelian Aharonov-Bohm scattering with each other. When there are more than three vortices in a system, the Aharonov-Bohm interaction, which is described by a path integral involving sums over elements of the braid group, becomes extremely complicated. The vortices are subject to a new kind of exotic statistics. The second part of the thesis discusses the physics that arises when the requirement that H be discrete is relaxed to allow H to have one continuous generator. The vortices or strings that result change the sign of the charge for charged particles. Loops of Alice string or pairs of vortices can carry charge without any apparent source. A quantization condition for the charge carried by such pairs and loops is derived. It is also found that loops of Alice string can carry magnetic charge and that topologically stable monopoles exist in any theory with Alice symmetry breaking.", "doi": "10.7907/5NNN-WN66", "publication_date": "1991", "thesis_type": "phd", "thesis_year": "1991" }, { "id": "thesis:2482", "collection": "thesis", "collection_id": "2482", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06062007-160632", "type": "thesis", "title": "Non-Conservation of Baryon Number at High Energy in the Standard Model", "author": [ { "family_name": "Espinosa", "given_name": "Olivier R.", "clpid": "Espinosa-Olivier-R" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Frautschi", "given_name": "Steven C.", "clpid": "Frautschi-S-C" }, { "family_name": "McKeown", "given_name": "Robert D.", "clpid": "McKeown-R-D" }, { "family_name": "Zachariasen", "given_name": "Fredrik", "clpid": "Zachariasen-F" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "We calculate the coupling constant and energy dependence of the scattering amplitudes for baryon- and lepton-number violating processes in the context of the standard model, in the semiclassical approximation. It is found that, to leading order in this expansion, the spin-averaged total cross sections for these processes grow as a power of the CM-energy and thus violate the bound imposed by unitarity. This result has a twofold implication: first, perturbation theory in the instanton sector of the electroweak theory must break down at high energies and, second, it strongly suggests that baryon and lepton number non-conservation might be observed experimentally at energies accesible in the near future.
", "doi": "10.7907/74cf-xv77", "publication_date": "1990", "thesis_type": "phd", "thesis_year": "1990" }, { "id": "thesis:2505", "collection": "thesis", "collection_id": "2505", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06072007-104420", "type": "thesis", "title": "Some Aspects of Open String Field Theories", "author": [ { "family_name": "Feng", "given_name": "Jiyu", "clpid": "Feng-Jiyu" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" }, { "family_name": "Gomez", "given_name": "Ricardo", "clpid": "Gomez-R" }, { "family_name": "Kavanagh", "given_name": "Ralph William", "clpid": "Kavanagh-R-W" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "The construction of covariant string field theories is an important step toward a deeper understanding of string theories. This thesis discusses the general formulation of bosonic and supersymmetric covariant open string field theories and their second quantization. A particular emphasis is given to the perturbative calculation in the framework of string field theory. The use of string wave functional and the technique of conformal field theory are illustrated by explicit calculations of on- and off-shell string amplitudes. The background independent cubic actions for open strings are described briefly.
", "doi": "10.7907/qgks-pd11", "publication_date": "1990", "thesis_type": "phd", "thesis_year": "1990" }, { "id": "thesis:8009", "collection": "thesis", "collection_id": "8009", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10242013-145903390", "primary_object_url": { "basename": "Yurtsever_1989.pdf", "content": "final", "filesize": 60435056, "license": "other", "mime_type": "application/pdf", "url": "/8009/1/Yurtsever_1989.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Singularities and Horizons in the Collisions of Gravitational Waves", "author": [ { "family_name": "Yurtsever", "given_name": "Ulvi Hamit", "clpid": "Yurtsever-Ulvi-Hamit" } ], "thesis_advisor": [ { "family_name": "Thorne", "given_name": "Kip S.", "clpid": "Thorne-K-S" } ], "thesis_committee": [ { "family_name": "Thorne", "given_name": "Kip S.", "clpid": "Thorne-K-S" }, { "family_name": "Phinney", "given_name": "E. Sterl", "orcid": "0000-0002-9656-4032", "clpid": "Phinney-E-S" }, { "family_name": "Schmidt", "given_name": "Maarten", "clpid": "Schmidt-M" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "local_group": [ { "literal": "TAPIR" }, { "literal": "Astronomy Department" }, { "literal": "div_pma" } ], "abstract": "This thesis presents a study of the dynamical, nonlinear interaction of colliding gravitational waves, as described by classical general relativity. It is focused mainly on two fundamental questions: First, what is the general structure of the singularities and Killing-Cauchy horizons produced in the collisions of exactly plane-symmetric gravitational waves? Second, under what conditions will the collisions of almost-plane gravitational waves (waves with large but finite transverse sizes) produce singularities?
\r\n\r\nIn the work on the collisions of exactly-plane waves, it is shown that Killing horizons in any plane-symmetric spacetime are unstable against small plane-symmetric perturbations. It is thus concluded that the Killing-Cauchy horizons produced by the collisions of some exactly plane gravitational waves are nongeneric, and that generic initial data for the colliding plane waves always produce \"pure\" spacetime singularities without such horizons. This conclusion is later proved rigorously (using the full nonlinear theory rather than perturbation theory), in connection with an analysis of the asymptotic singularity structure of a general colliding plane-wave spacetime. This analysis also proves that asymptotically the singularities created by colliding plane waves are of inhomogeneous-Kasner type; the asymptotic Kasner axes and exponents of these singularities in general depend on the spatial coordinate that runs tangentially to the singularity in the non-plane-symmetric direction.
\r\n\r\nIn the work on collisions of almost-plane gravitational waves, first some general properties of single almost-plane gravitational-wave spacetimes are explored. It is shown that, by contrast with an exact plane wave, an almost-plane gravitational wave cannot have a propagation direction that is Killing; i.e., it must diffract and disperse as it propagates. It is also shown that an almost-plane wave cannot be precisely sandwiched between two null wavefronts; i.e., it must leave behind tails in the spacetime region through which it passes. Next, the occurrence of spacetime singularities in the collisions of almost-plane waves is investigated. It is proved that if two colliding, almost-plane gravitational waves are initially exactly plane-symmetric across a central region of sufficiently large but finite transverse dimensions, then their collision produces a spacetime singularity with the same local structure as in the exact-plane-wave collision. Finally, it is shown that a singularity still forms when the central regions are only approximately plane-symmetric initially. Stated more precisely, it is proved that if the colliding almost-plane waves are initially sufficiently close to being exactly plane-symmetric across a bounded central region of sufficiently large transverse dimensions, then their collision necessarily produces spacetime singularities. In this case, nothing is now known about the local and global structures of the singularities.
", "doi": "10.7907/zm5n-g882", "publication_date": "1989", "thesis_type": "phd", "thesis_year": "1989" }, { "id": "thesis:7405", "collection": "thesis", "collection_id": "7405", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01172013-140801181", "primary_object_url": { "basename": "Cline_jm_1988.pdf", "content": "final", "filesize": 19563218, "license": "other", "mime_type": "application/pdf", "url": "/7405/1/Cline_jm_1988.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Effective Lagrangians and Infinity Cancellations for Open String Theories", "author": [ { "family_name": "Cline", "given_name": "James Michael", "clpid": "Cline-James-Michael" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Peck", "given_name": "Charles W.", "clpid": "Peck-C-W" }, { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" }, { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "The covariant path integral formalism for theories of open and closed strings is\r\nused to study the first order of string perturbation theory beyond tree level for the\r\nclosed-string states, in which the string world sheet has the topology of the disk or the\r\nreal projective plane. We find that scattering amplitudes (in flat spacetime) confirm\r\nthese surfaces' contribution to the low-energy effective action for the bosonic string\r\ntheory, as derived by another method, demanding consistency of string propagation in\r\nbackground gravitational and dilaton fields (the \"sigma model approach\"). However,\r\nwe are not able to obtain results consistent with this effective action by demanding\r\nthat amplitudes in a curved background be finite; this is an unresolved puzzle. Decoupling\r\nof spurious tachyon states from the superstring S-matrix is discussed, and\r\nfiniteness of amplitudes for the disk plus projective plane is demonstrated for a large\r\nclass of external states, when the gauge group is SO(32).
", "doi": "10.7907/9vpf-s680", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:7495", "collection": "thesis", "collection_id": "7495", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:02252013-121827558", "type": "thesis", "title": "GUT Monopole Detection with Scintillator", "author": [ { "family_name": "Lane", "given_name": "Charles E.", "clpid": "Lane-Charles-E" } ], "thesis_advisor": [ { "family_name": "Barish", "given_name": "Barry C.", "orcid": "0000-0001-6386-7371", "clpid": "Barish-B-C" } ], "thesis_committee": [ { "family_name": "Barish", "given_name": "Barry C.", "orcid": "0000-0001-6386-7371", "clpid": "Barish-B-C" }, { "family_name": "Peck", "given_name": "Charles W.", "clpid": "Peck-C-W" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Prince", "given_name": "Thomas A.", "orcid": "0000-0002-8850-3627", "clpid": "Prince-T-A" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Searches for the monopoles predicted by Grand Unified Theories (GUTs) have required new approaches, since these monopoles should be both slow and highly penetrating. The ability of scintillator to respond to particles of velocity < 10\u207b\u00b3 c has been demonstrated, indicating that scintillator detectors should be useful in GUT monopole searches.
\r\n\r\nA small monopole detector prototype at the Earth's surface was operated in an effort to understand the problems and possibilities of monopole detection. The design philosophy, techniques, and the lessons learned from the prototype detector could then be applied to much larger monopole detectors. The prototype was not able to set new limits for the GUT monopole flux in cosmic rays, but in a more general analysis it was found that new limits could be set on the flux of lightly ionizing particles of mass ~ 10\u00b9\u2070 GeV.
\r\n\r\nWhen GUT monopole detectors are scaled up to the size needed to challenge astrophysical limits, it becomes more likely that a flux could be found. This motivates a more careful examination of the scintillator counters, since their signal should be clear and unambiguous for a monopole candidate. The performance of the liquid scintillator counters for the MACRO (Monopole And Cosmic Ray Observatory) experiment was given considerable scrutiny, both to try to understand the observed behavior of these counters, and also to improve them for monopole detection.
\r\n\r\nThe results of these tests indicate that MACRO should be able either to establish a monopole flux or to limit it to a small fraction of the 'missing mass' of the universe.
\r\n", "doi": "10.7907/TYAF-0T74", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:7508", "collection": "thesis", "collection_id": "7508", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:03112013-144150219", "primary_object_url": { "basename": "Kiritsis-eb-1988.pdf", "content": "final", "filesize": 31350266, "license": "other", "mime_type": "application/pdf", "url": "/7508/1/Kiritsis-eb-1988.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Topics in Conformal Field Theory", "author": [ { "family_name": "Kiritsis", "given_name": "Elias B.", "clpid": "Kiritsis-Elias-B" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" }, { "family_name": "Simon", "given_name": "Barry M.", "orcid": "0000-0003-2561-8539", "clpid": "Simon-B" }, { "family_name": "Barish", "given_name": "Barry C.", "orcid": "0000-0001-6386-7371", "clpid": "Barish-B-C" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "In this work two major topics in Conformal Field Theory are discussed. First a detailed investigation of N=2 Superconformal theories is presented. The structure of the representations of the N=2 superconformal algebras is investigated and the character formulae are calculated. The general structure of N=2 superconformal theories is elucidated and the operator algebra of the minimal models is derived. The first minimal system is discussed in more detail. Second, applications of the conformal techniques are studied in the Ashkin-Teller model. The c = 1 as well as the c = \u00bd critical lines are discussed in detail.
\r\n", "doi": "10.7907/xp2b-x462", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:7526", "collection": "thesis", "collection_id": "7526", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:03192013-082028179", "primary_object_url": { "basename": "Liu_g_1988.pdf", "content": "final", "filesize": 16637767, "license": "other", "mime_type": "application/pdf", "url": "/7526/1/Liu_g_1988.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "In Search of Slow-Moving Ionizing Massive Particles", "author": [ { "family_name": "Liu", "given_name": "Gang", "clpid": "Liu-Gang" } ], "thesis_advisor": [ { "family_name": "Barish", "given_name": "Barry C.", "orcid": "0000-0001-6386-7371", "clpid": "Barish-B-C" } ], "thesis_committee": [ { "family_name": "Barish", "given_name": "Barry C.", "orcid": "0000-0001-6386-7371", "clpid": "Barish-B-C" }, { "family_name": "Drever", "given_name": "Ronald W. P.", "clpid": "Drever-R-W-P" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Porter", "given_name": "Frank C.", "orcid": "0000-0003-1948-8889", "clpid": "Porter-F-C" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Many particles proposed by theories, such as GUT monopoles, nuclearites and 1/5 charge superstring particles, can be categorized as Slow-moving, Ionizing, Massive Particles (SIMPs).
\r\n\r\nDetailed calculations of the signal-to-noise ratios in vanous acoustic and mechanical methods for detecting such SIMPs are presented. It is shown that the previous belief that such methods are intrinsically prohibited by the thermal noise is incorrect, and that ways to solve the thermal noise problem are already within the reach of today's technology. In fact, many running and finished gravitational wave detection ( GWD) experiments are already sensitive to certain SIMPs. As an example, a published GWD result is used to obtain a flux limit for nuclearites.
\r\n\r\nThe result of a search using a scintillator array on Earth's surface is reported. A flux limit of 4.7 x 10\u207b\u00b9\u00b2 cm\u207b\u00b2 sr\u207b\u00b9 s\u207b\u00b9 (90% c.l.) is set for any SIMP with 2.7 x 10\u207b\u2074 < \u03b2 < 5 x 10\u207b\u00b3 and ionization greater than 1/3 of minimum ionizing muons. Although this limit is above the limits from underground experiments for typical supermassive particles (10\u00b9\u2076 GeV), it is a new limit in certain \u03b2 and ionization regions for less massive ones (~10\u2079 GeV) not able to penetrate deep underground, and implies a stringent limit on the fraction of the dark matter that can be composed of massive electrically and/or magnetically charged particles.
\r\n\r\nThe prospect of the future SIMP search in the MACRO detector is discussed. The special problem of SIMP trigger is examined and a circuit proposed, which may solve most of the problems of the previous ones proposed or used by others and may even enable MACRO to detect certain SIMP species with \u03b2 as low as the orbital velocity around the earth.
\r\n\r\n", "doi": "10.7907/nqqm-xy79", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:3179", "collection": "thesis", "collection_id": "3179", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-08202008-083708", "type": "thesis", "title": "G/H Conformal Field Theory", "author": [ { "family_name": "Douglas", "given_name": "Michael Ronald", "clpid": "Douglas-Michael-Ronald" } ], "thesis_advisor": [ { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" } ], "thesis_committee": [ { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Fox", "given_name": "Geoffrey C.", "clpid": "Fox-G-C" }, { "family_name": "Porter", "given_name": "Frank C.", "orcid": "0000-0003-1948-8889", "clpid": "Porter-F-C" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "We show that for every affine Lie algebra G and subalgebra H there exists an exactly solvable two-dimensional conformal field theory, and give a procedure for explicitly determining its correlation functions and partition function given those for the Wess-Zumino-Witten models with symmetry algebras G and H.
", "doi": "10.7907/YNEZ-8X17", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:7420", "collection": "thesis", "collection_id": "7420", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01222013-110618869", "type": "thesis", "title": "A Search for Double Beta Decay in \u2077\u2076Ge", "author": [ { "family_name": "Fisher", "given_name": "Peter Harrison", "clpid": "Fisher-Peter-Harrison" } ], "thesis_advisor": [ { "family_name": "Boehm", "given_name": "Felix H.", "clpid": "Boehm-F-H" } ], "thesis_committee": [ { "family_name": "Boehm", "given_name": "Felix H.", "clpid": "Boehm-F-H" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Newman", "given_name": "Harvey B.", "orcid": "0000-0003-0964-1480", "clpid": "Newman-H-B" }, { "family_name": "Filippone", "given_name": "Bradley W.", "orcid": "0000-0002-2618-2688", "clpid": "Filippone-B-W" }, { "family_name": "Vogel", "given_name": "Petr", "orcid": "0000-0003-0587-5466", "clpid": "Vogel-P" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis describes a search for the double beta (\u03b2\u03b2) decay of \u2077\u2076Ge using an\r\narray of eight high purity, high resolution germanium detectors containing a total\r\nof 3.9 x 10\u00b2\u2074 \u2077\u2076Ge nuclei. There are three modes of \u03b2\u03b2 decay: neutrinoless (0\u0475)\u03b2\u03b2\r\ndecay, \u03b2\u03b2 decay with Majoron emission (x\u2070\u03b2\u03b2 decay) and two neutrino (2\u0475)\u03b2\u03b2\r\ndecay. The first two modes violate lepton number conservation, while the third is\r\nallowed by the Standard Model. 0\u0475\u03b2\u03b2 decay may take place to the ground state of\r\nthe daughter nucleus (0\u207a \u2192 0\u207a transition) or to an excited state of the daughter\r\nnucleus (0\u207a \u2192 2\u207a transition). The detector was operated for a total time of 2033 h\r\n(0.23 y) which translates to 1.30 kg-y. The background at the \u03b2\u03b2 decay transition\r\nenergy was 0.53 counts keV\u207b\u00b9 y\u207b\u00b9 (10\u00b2\u00b3 \u2077\u2076Ge nuclei)\u207b\u00b9. No evidence for double beta\r\ndecay of any sort was found and the half life limits are T0\u0475\u00bd(0\u207a \u2192 0\u207a) > 1.2 x 10\u00b2\u00b3 y, \r\nT0\u0475\u00bd(0\u207a \u2192 2\u207a) > 2 x 10\u00b2\u00b2 y, T\u03c7o\u00bd > 8 x 10\u00b2\u2070 y, and T2\u0475\u00bd > 2 x 10\u00b2\u2070 y, all at 90% c.l. \r\nThe limit for the neutrinoless mode translates to an upper limit of between 16 and\r\n1.6 eV on the Majorana mass of the neutrino, depending on the nuclear matrix\r\nelement used.
\r\n", "doi": "10.7907/fmvr-y629", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:7402", "collection": "thesis", "collection_id": "7402", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01172013-111439406", "type": "thesis", "title": "The Singular Mechanics of Particles and Strings", "author": [ { "family_name": "Allen", "given_name": "Theodore John", "clpid": "Allen-Theodore-John" } ], "thesis_advisor": [ { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" } ], "thesis_committee": [ { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" }, { "family_name": "Frautschi", "given_name": "Steven C.", "clpid": "Frautschi-S-C" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Peck", "given_name": "Charles W.", "clpid": "Peck-C-W" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "The quantum mechanics of singular systems is a topic of considerable importance for all the theories of elementary particle physics in which gauge invariance is a universal attribute. This is especially true for string theories which are gauge theories par excellence.
\r\n\r\nThis thesis begins with a brief exposition of singular Hamiltonian mechanics. This tool is applied principally to manifestly supersymmetric particle and string theories. The Dirac particle and the bosonic particle and string are briefly examined. In particular, a method is shown for quantizing the point superparticle in four and ten dimensions. The two actions proposed for describing the manifestly supersymmetric string are shown to be essentially equivalent. The problems of their quantization are briefly discussed.
", "doi": "10.7907/hvjy-be63", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:7486", "collection": "thesis", "collection_id": "7486", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:02202013-144403198", "primary_object_url": { "basename": "Morris 1988.pdf", "content": "final", "filesize": 18679212, "license": "other", "mime_type": "application/pdf", "url": "/7486/1/Morris 1988.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "The R +\u025bR\u00b2 Cosmology", "author": [ { "family_name": "Morris", "given_name": "Michael Scott", "clpid": "Morris-Michael-Scott" } ], "thesis_advisor": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "thesis_committee": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" }, { "family_name": "Phinney", "given_name": "E. Sterl", "orcid": "0000-0002-9656-4032", "clpid": "Phinney-E-S" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Phillips", "given_name": "Thomas G.", "clpid": "Phillips-T-G" } ], "local_group": [ { "literal": "TAPIR" }, { "literal": "Astronomy Department" }, { "literal": "div_pma" } ], "abstract": "This thesis presents the study of a model cosmology based on the R +\u025bR\u00b2 gravitational Lagrangian. It may be roughly divided into two distinct parts. First, the classical inflationary scenario is developed. Then, the formalism of quantum cosmology is employed to determine initial conditions for the classical model.
\r\n\r\nIn the work on the classical model, the evolution equations for an isotropic and homogeneous universe are solved to exhibit both early-time inflation and a smooth transition to subsequent radiation-dominated behavior. Then perturbations on this isotropic background are evolved through the model to provide constraints on the model parameters from the observational limits on anisotropy today. This study concludes that such an inflationary model will prove a viable description for our universe if the initial Hubble parameter Hi is bounded from below, Hi > 10\u207b\u2075 lPl\u207b\u00b9, and if \u025b > 10\u00b9\u00b9 lPl\u00b2.
\r\n\r\nIn the work on the wave function, the two boundary conditions of Vilenkin (\"tunneling from nothing\") and Hartle and Hawking (\"no boundary\") are compared. The wave functions obtained are restricted to the initial edge of classical Lorentzian inflationary trajectories as distributions over initial conditions for the classical inflationary model. It is found that Vilenkin's wave function prefers the universe to undergo a great deal of inflation, whereas Hartle and Hawking's wave function prefers the universe to undergo little inflation. Finally, both boundary conditions are shown to require that inhomogeneous perturbative modes start out in their ground states.
", "doi": "10.7907/h44f-9639", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:11466", "collection": "thesis", "collection_id": "11466", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04152019-155658415", "type": "thesis", "title": "The Regularisation and Renormalisation of Gauge Theories", "author": [ { "family_name": "Warr", "given_name": "Brian John", "clpid": "Warr-Brian-John" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Simon", "given_name": "Barry M.", "orcid": "0000-0003-2561-8539", "clpid": "Simon-B" }, { "family_name": "Peck", "given_name": "Charles W.", "clpid": "Peck-C-W" }, { "family_name": "Politzer", "given_name": "Hugh David", "orcid": "0000-0002-4983-6621", "clpid": "Politzer-H-D" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "The method of effective Lagrangian flow provides the most physically illuminating discussion of renormalisation theory. At distance scales much larger than some physical cutoff, the physics is described by a small number of parameters, which can be identified purely by dimensional analysis. For scalar theories a rigorous yet simple proof of renormalisability, based on this concept, was given by Polchinski, and this work forms the bedrock of this thesis.
\r\n\r\nFor gauge theories there is the extra issue of the unitarity of the renormalised S-matrix, which can only be guaranteed by proving renormalised Ward identities, and this is what we carry out for all cases of interest in d = 4. In particular we cover the case of N = 1 super Yang-Mills.
\r\n\r\nWe prove that the cancellation of anomalies at the one-loop level is a sufficient as well as necessary condition for a theory to be perturbatively quantisable, and hence that there are no higher-loop anomalies.
", "doi": "10.7907/yzgs-4f82", "publication_date": "1987", "thesis_type": "phd", "thesis_year": "1987" }, { "id": "thesis:10358", "collection": "thesis", "collection_id": "10358", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:08012017-135315454", "primary_object_url": { "basename": "Hamidi_s_1987.pdf", "content": "final", "filesize": 29867052, "license": "other", "mime_type": "application/pdf", "url": "/10358/1/Hamidi_s_1987.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Interactions of Strings Compactified on Orbifolds", "author": [ { "family_name": "Hamidi", "given_name": "Shahram", "clpid": "Hamidi-Shahram" } ], "thesis_advisor": [ { "family_name": "Frautschi", "given_name": "Steven C.", "clpid": "Frautschi-S-C" } ], "thesis_committee": [ { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Fox", "given_name": "Geoffrey C.", "clpid": "Fox-G-C" }, { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" }, { "family_name": "Frautschi", "given_name": "Steven C.", "clpid": "Frautschi-S-C" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "It is very important to understand the process of string compactification before one can extract any reliable phenomenology. We consider an exactly solvable method of string compactification, in which the internal space is an orbifold. We compute various interaction amplitudes and describe how other amplitudes can be calculated.
\r\n\r\nMulti-valued string variables are handled by formulating the amplitudes on covering spaces where they become single-valued. In the computation of the amplitudes, stretched string intermediate states give rise to expressions that are non-perturbative from the non-linear sigma model point of view.
\r\n\r\nWe also discuss, in the context of Z orbifold, the \"blowing up\" of the fixed points of an orbifold, to give rise to a Calabi-Yau manifold. The resulting Calabi-Yau manifold is shown to be non-perturbatively stable.
", "doi": "10.7907/gvyt-8e89", "publication_date": "1987", "thesis_type": "phd", "thesis_year": "1987" }, { "id": "thesis:11811", "collection": "thesis", "collection_id": "11811", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10112019-085854195", "type": "thesis", "title": "Lattice Gauge Theory on a Parallel Computer", "author": [ { "family_name": "Flower", "given_name": "Jonathan William", "clpid": "Flower-Jonathan-William" } ], "thesis_advisor": [ { "family_name": "Fox", "given_name": "Geoffrey C.", "clpid": "Fox-G-C" } ], "thesis_committee": [ { "family_name": "Fox", "given_name": "Geoffrey C.", "clpid": "Fox-G-C" }, { "family_name": "Koonin", "given_name": "Steven E.", "orcid": "0000-0001-5897-5319", "clpid": "Koonin-S-E" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Peck", "given_name": "Charles W.", "clpid": "Peck-C-W" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "The results of several numerical simulations of QCD by Monte Carlo lattice gauge theory are presented. Studying the mesonic potential on a 204 lattice, we conclude that asymptotic scaling does not hold over the range 6.1 \u2264 \u03b2 \u2264 6.7, although we are not able to quantify the discrepencies. The effect of discrete rotational symmetry on physical parameters is examined and seems to modify the string tension by 15 % at \u03b2 = 6.1, while at \u03b2 = 6.3 the change was less than 1 %. The potential between three charges is studied and yields a string tension of .18 GeV2, consistent with mesonic calculations and relativised potential models. Contributions to the potential from low-energy string vibrations appear small in the range x \u227e .5 fm. We perform energy density measurements in the colour fields surrounding both mesons and baryons, which provide strong evidence in favour of the dual superconductor picture of confinement. It is also suggested that the confining strings in the baryon meet at a central point rather than joining the quarks pairwise.
\r\n\r\nSeveral algorithms are explored in an attempt to develop simulation methods which are able to directly account for the currents generated by colour sources. The extension of the Langevin equation to complex degrees of freedom is derived leading to a Fokker-Planck equation for a complex 'Probability distribution'. Using this technique we are then able to calculate energy densities in U(1) gauge theory at-large charge separations. The extension of the method to non-Abelian theories comes up against an unresolved problem in segregation for certain types of observable.
\r\n\r\nWe discuss methods for the simulation of full QCD, including the effects of dynamical fermions. The Langevin approach is analysed in detail, and the systematic error associated with the discretisation of the equations of motion is derived. We propose a mixed Langevin/Metropolis algorithm and explore its properties on a small lattice. Finally, the method is tested on the finite temperature deconfinement transition and applied to the mesonic potential. It is found that shielding effects lead to deconfinement at \u03b2 = 6.1 on a lattice of size 122 x 162.
", "doi": "10.7907/zhdg-qp82", "publication_date": "1987", "thesis_type": "phd", "thesis_year": "1987" }, { "id": "thesis:10359", "collection": "thesis", "collection_id": "10359", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:08022017-083105707", "type": "thesis", "title": "Quantum and Inflationary Cosmology with Higher Derivative Gravity", "author": [ { "family_name": "Miji\u0107", "given_name": "Milan B.", "orcid": "0000-0001-5095-8469", "clpid": "Miji\u0107-Milan-B" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Gell-Mann", "given_name": "Murray", "clpid": "Gell-Mann-M" }, { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" }, { "family_name": "Peck", "given_name": "Charles W.", "clpid": "Peck-C-W" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "The subject of this thesis is the description of the Very Early Universe, from the Big Bang to the beginning of the radiation-dominated Friedman-Roberston-Walker era. We examine a pure gravity inflationary model for the Universe which is based on adding \u0190R2 term to the usual gravitational Lagrangian (\"improved Starobinsky model\"). We find the classical inflationary solution essentially independent of initial conditions. The model has only one free parameter, which is bounded from above by observational constraints on scalar and tensorial perturbations and from below by both the need for standard baryogenesis and the need for galaxy formation. This requires 1011GeV < \u0190-1/2 < 1013GeV.
\r\n\r\nThe model is interpreted as a Chaotic Inflationary model, with initial conditions for classical evolution being generated by the quantum fluctuations in metric and curvature in Very Early Universe. We discuss those fluctuations using a particular solution of the Wheeler-De Witt equation and find that the inflationary phase is a highly typical event.
", "doi": "10.7907/1sz4-gt36", "publication_date": "1987", "thesis_type": "phd", "thesis_year": "1987" }, { "id": "thesis:7421", "collection": "thesis", "collection_id": "7421", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01222013-133723975", "primary_object_url": { "basename": "Polychronakos 1987.pdf", "content": "final", "filesize": 27070215, "license": "other", "mime_type": "application/pdf", "url": "/7421/1/Polychronakos 1987.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Anomalous Quantum Mumbers and Topological Properties of Field Theories", "author": [ { "family_name": "Polychronakos", "given_name": "Alexios P.", "clpid": "Polychronakos-Alexios-P" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Simon", "given_name": "Barry M.", "orcid": "0000-0003-2561-8539", "clpid": "Simon-B" }, { "family_name": "Cross", "given_name": "Michael Clifford", "clpid": "Cross-M-C" }, { "family_name": "Zachariasen", "given_name": "Fredrik", "clpid": "Zachariasen-F" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "We examine the connection between anomalous quantum numbers, symmetry breaking patterns and topological properties of some field theories. The main results are the following: In three dimensions the vacuum in the presence of abelian magnetic field configurations behaves like a superconductor. Its quantum numbers are exactly calculable and are connected with the Atiyah-Patodi-Singer index theorem. Boundary conditions, however, play a nontrivial role in this case. Local conditions were found to be physically preferable than the usual global ones. Due to topological reasons, only theories for which the gauge invariant photon mass in three dimensions obeys a quantization condition can support states of nonzero magnetic flux. For similar reasons, this mass induces anomalous angular momentum quantum numbers to the states of the theory. Parity invariance and global flavor symmetry were shown to be incompatible in such theories. In the presence of massless flavored fermions, parity will always break for an odd number of fermion flavors, while for even fermion flavors it may not break but only at the expense of maximally breaking the flavor symmetry. Finally, a connection between these theories and the quantum Hall effectwas indicated.
\r\n", "doi": "10.7907/PBQR-B016", "publication_date": "1987", "thesis_type": "phd", "thesis_year": "1987" }, { "id": "thesis:10362", "collection": "thesis", "collection_id": "10362", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:08042017-154857683", "primary_object_url": { "basename": "Siopsis_G_1987.pdf", "content": "final", "filesize": 34068377, "license": "other", "mime_type": "application/pdf", "url": "/10362/1/Siopsis_G_1987.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Some Aspects of the Quantization of Theories with a Gauge Invariance", "author": [ { "family_name": "Siopsis", "given_name": "George", "clpid": "Siopsis-George" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Peck", "given_name": "Charles W.", "clpid": "Peck-C-W" }, { "family_name": "Schwarz", "given_name": "John H.", "orcid": "0000-0001-9861-7559", "clpid": "Schwarz-J-H" }, { "family_name": "Zachariasen", "given_name": "Fredrik", "clpid": "Zachariasen-F" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "We discuss some problems that arise when one tries to quantize a theory that possesses gauge degrees of freedom. First, we identify the Gribov problem that is encountered when the Faddeev-Popov procedure of fixing the gauge is employed to define a perturbation expansion. We propose a modification of the procedure that takes this problem into account. We then apply this method to two-dimensional gauge theories where the exact answer is known. Second, we try to build chiral theories that are consistent in the presence of anomalies, without making use of additional degrees of freedom. We are able to solve the model exactly in two dimensions, arriving at a gauge-invariant theory. We discuss the four-dimensional case and also the application of this method to string theory. In the latter, we obtain a model that lives in arbitrary dimensions. However, we do not compute the spectrum of the model. Third, we investigate the possibility of compactifying the unwanted dimensions of superstrings on a group manifold. We give a complete list of conformally invariant models. We also discuss one-loop modular invariance. We consider both type-II and heterotic superstring theories. Fourth, we discuss quantization of string field theory. We start by presenting the lagrangian approach, to demonstrate the non-uniqueness of the measure in the path-integral. It is fixed by demanding unitarity, which manifests itself in the hamiltonian formulation, studied next.
", "doi": "10.7907/hf4w-dw98", "publication_date": "1987", "thesis_type": "phd", "thesis_year": "1987" }, { "id": "thesis:11438", "collection": "thesis", "collection_id": "11438", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04032019-174006406", "type": "thesis", "title": "The \u0394I = 1/2 Rule and the Strong Coupling Expansion", "author": [ { "family_name": "Angus", "given_name": "Ian Gareth", "clpid": "Angus-Ian-Gareth" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Politzer", "given_name": "Hugh David", "orcid": "0000-0002-4983-6621", "clpid": "Politzer-H-D" }, { "family_name": "Newman", "given_name": "Harvey B.", "orcid": "0000-0003-0964-1480", "clpid": "Newman-H-B" }, { "family_name": "Cross", "given_name": "Michael Clifford", "clpid": "Cross-M-C" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "We will attempt to understand the Delta I Equals One Half pattern of the nonleptonic weak decays of the Kaons. The calculation scheme employed is the Strong Coupling Expansion of lattice QCD. Kogut-Susskind fermions are used in the Hamiltonian formalism. We will describe in detail the methods used to expedite this calculation, almost all of which was done by computer algebra.
\r\n\r\nThe final result is very encouraging. Even though an exact interpretation is clouded by the presence of irrelevant operators, a distinct signal of the Delta I Equals One Half is observed. With an appropriate choice of the one free parameter, enhancements as great as those observed experimentally can be obtained along with a qualitative prediction for the relative magnitudes of the CP violating phases.
\r\n\r\nWe also point out a number of surprising results which we turn up in the course of the calculation. The computer methods employed are briefly described.
", "doi": "10.7907/2188-5x19", "publication_date": "1986", "thesis_type": "phd", "thesis_year": "1986" }, { "id": "thesis:11470", "collection": "thesis", "collection_id": "11470", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04162019-142819748", "type": "thesis", "title": "Charged Kaon Production in Tau Lepton Decays", "author": [ { "family_name": "Mills", "given_name": "Geoffrey Blount", "clpid": "Mills-Geoffrey-Blount" } ], "thesis_advisor": [ { "family_name": "Barish", "given_name": "Barry C.", "orcid": "0000-0001-6386-7371", "clpid": "Barish-B-C" } ], "thesis_committee": [ { "family_name": "Barish", "given_name": "Barry C.", "orcid": "0000-0001-6386-7371", "clpid": "Barish-B-C" }, { "family_name": "Gomez", "given_name": "Ricardo", "clpid": "Gomez-R" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Phillips", "given_name": "Thomas G.", "clpid": "Phillips-T-G" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "The result of an experiment performed at the PEP e+e- storage ring which\r\noperated at 29.0 GeV/c2 is presented. The DELCO detector, which emphasizes\r\nCherenkov particle identification, is used to measured the production of charged\r\nkaons in \u03c4 decays. The branching ratio of the Cabibbo-suppressed decays b(\u03c4\u00b1 \u2192\r\nK\u00b1 \u03bd\u03c4) = (0.57 \u00b1 0.15)%, b(\u03c4\u00b1 \u2192 K\u00b1 \u03bd\u03c4 + n\u03c00) = (1.59 \u00b1 0.23)% n \u2265 0, and\r\nb(\u03c4\u00b1 \u2192 K\u00b1\u03c0+\u03c0-\u03bd\u03c4(\u03c00)) = (0.22+0.16-0.13)% are measured, and the branching ratio\r\nof the Cabibbo-favored decay b(\u03c4\u00b1 \u2192 K+K-\u03c0\u00b1\u03bd\u03c4) = (0.22+0.17-0.11)% is measured.\r\nThese branching ratio measurements provide a test e - \u00b5 - \u03c4 universality and are\r\nin agreement with and the predictions of SU(3) sum rules. The invariant mass\r\ndistribution of the K+K-\u03c0 system in the exclusive \u03c4\u00b1 \u2192 K+K-\u03c0\u00b1\u03bd\u03c4 channel is\r\nused to set a limit of 157 MeV/c2 at 95% CL on the \u03c4 neutrino mass.
", "doi": "10.7907/n2rv-ma10", "publication_date": "1986", "thesis_type": "phd", "thesis_year": "1986" }, { "id": "thesis:11447", "collection": "thesis", "collection_id": "11447", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04052019-170528187", "type": "thesis", "title": "Gauge Fields in the Functional Schr\u00f6dinger Representation", "author": [ { "family_name": "Hatfield", "given_name": "Brian F.", "clpid": "Hatfield-Brian-F" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Peck", "given_name": "Charles W.", "clpid": "Peck-C-W" }, { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Prince", "given_name": "Thomas A.", "orcid": "0000-0002-8850-3627", "clpid": "Prince-T-A" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "We explore gauge fields in the functional Schr\u00f6dinger representation. We first consider perturbatively solving quantum electrodynamics using known free field wave functionals. Failures of ordinary perturbative techniques force us to develop techniques to solve nontrivial functional differential equations. These techniques can also be used for Yang-Mills as we also demonstrate. We regularize QED in a new fashion using functional directional derivatives. This may also be generalized to Yang-Mills. We carry out mass renormalization in QED using wave functionals since no one has explicitly done it before. We briefly look at magnetic flux tubes in the Abelian Higgs model to illustrate renormalization in a variational calculation. We also perform a variational calculation using wave functionals in Yang-Mills to see if quantum fluctuations can produce electric flux tubes.
", "doi": "10.7907/ys3x-qz72", "publication_date": "1986", "thesis_type": "phd", "thesis_year": "1986" }, { "id": "thesis:11348", "collection": "thesis", "collection_id": "11348", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01222019-093733020", "primary_object_url": { "basename": "Caticha Alfonso_N_1985.pdf", "content": "final", "filesize": 17548721, "license": "other", "mime_type": "application/pdf", "url": "/11348/1/Caticha Alfonso_N_1985.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Limit Theorems for Classical Spin Systems with an Abelian Discrete Symmetry", "author": [ { "family_name": "Caticha Alfonso", "given_name": "Nestor", "orcid": "0000-0002-7446-6765", "clpid": "Caticha-Alfonso-Nestor" } ], "thesis_advisor": [ { "family_name": "Simon", "given_name": "Barry M.", "orcid": "0000-0003-2561-8539", "clpid": "Simon-B" } ], "thesis_committee": [ { "family_name": "Simon", "given_name": "Barry M.", "orcid": "0000-0003-2561-8539", "clpid": "Simon-B" }, { "family_name": "Peck", "given_name": "Charles W.", "clpid": "Peck-C-W" }, { "family_name": "Cross", "given_name": "Michael Clifford", "clpid": "Cross-M-C" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Classical spin models with a discrete abelian symmetry (Zp) are studied and compared to analogous models with a continuous (0(2)) symmetry.
\r\n\r\nThe dependence on p (the number of states) of some quantities, e.g ., the pressure and correlation functions, is studied. For high p, under fairly general conditions, the pressure of the Zp invariant model converges exponentially, in p, to that of the 0(2) model. Results of a similar nature, although obtained under more restrictive conditions, are presented for a class of expectation values.
\r\n\r\nSeveral different methods of proving Mermin- and Wagner-like results are reviewed and it is suggested that these methods are not sufficiently powerful to be used in obtaining upper bounds on the magnetization temperature of the two dimensional Zp model. A rigorous lower bound is obtained using a Peierls-Chessboard method.
", "doi": "10.7907/yyxh-p706", "publication_date": "1985", "thesis_type": "phd", "thesis_year": "1985" }, { "id": "thesis:11354", "collection": "thesis", "collection_id": "11354", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01222019-150217091", "primary_object_url": { "basename": "Markey_JK_1985.pdf", "content": "final", "filesize": 17846374, "license": "other", "mime_type": "application/pdf", "url": "/11354/1/Markey_JK_1985.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Transverse Polarization of Beta Particles from Polarized Nuclei", "author": [ { "family_name": "Markey", "given_name": "John Kevin", "clpid": "Markey-John-Kevin" } ], "thesis_advisor": [ { "family_name": "Boehm", "given_name": "Felix H.", "clpid": "Boehm-F-H" } ], "thesis_committee": [ { "family_name": "Boehm", "given_name": "Felix H.", "clpid": "Boehm-F-H" }, { "family_name": "Feynman", "given_name": "Richard Phillips", "clpid": "Feynman-R-P" }, { "family_name": "Barnes", "given_name": "Charles A.", "clpid": "Barnes-C-A" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "In this thesis an experiment to measure the transverse polarization of electrons from the decay of polarized 60Co is presented. The result
\r\n\r\n[equation; see abstract in scanned thesis for details]
\r\n\r\nis consistent with the predicted polarization based on the V - A theory of the weak interaction and the Weinberg, Salam, Glashow model. The theoretical prediction is
\r\n\r\n[equation; see abstract in scanned thesis for details]
\r\n\r\nwhere
\r\n\r\n[equation; see abstract in scanned thesis for details].
\r\n\r\nThis is the first measurement of the transverse polarization of beta particles from the decay of polarized nuclei. The polarization of the electrons was measured by scattering them from gold foil and detecting the scattering asymmetry predicted by Mott scattering theory. 60Co nuclei were polarized by embedding them in a ferromagnetic host where they feel a strong hyperfine field. The host foil was attached to a dilution refrigerator to lower the entropy of the nuclei and allow for nuclear polarization.
", "doi": "10.7907/dcqv-yv75", "publication_date": "1985", "thesis_type": "phd", "thesis_year": "1985" }, { "id": "thesis:10363", "collection": "thesis", "collection_id": "10363", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:08042017-160047213", "type": "thesis", "title": "Chiral Perturbation Theory and the Weak Interaction", "author": [ { "family_name": "Bijnens", "given_name": "Johan Lambert", "orcid": "0000-0002-1618-2844", "clpid": "Bijnens-Johan-Lambert" } ], "thesis_advisor": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" } ], "thesis_committee": [ { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Hitlin", "given_name": "David G.", "orcid": "0000-0003-4028-6982", "clpid": "Hitlin-D-G" }, { "family_name": "Cowan", "given_name": "Eugene W.", "clpid": "Cowan-E-W" } ], "local_group": [ { "literal": "Caltech Theory" }, { "literal": "div_pma" } ], "abstract": "We study the interface between the standard six-quark model and the observed low-energy weak phenomena. The main processes discussed are weak decays of kaons and hyperons. We study first the low-energy effective weak Hamiltonian at the quark level. This is derived using the renormalization group in leading logarithmic approximation.
\r\n\r\nThen some properties of this effective weak Hamiltonian that can be derived using chiral perturbation theory are studied. A review of chiral perturbation theory is included.
\r\n\r\nThis formalism is used to study the relation between K̅0K0 mixing and a \u0394I = 3/2 decay. We find that the logarithmic corrections to this relation are large, making it unreliable. The same formalism is used to discuss a relation between K\u03c0\u03c0, K\u03c0 and K-vacuum matrix elements used in most attempts to compute the K\u03c0\u03c0 matrix element relevant for the \u0394I = 1/2 rule. The domain of validity of this relation is determined.
\r\n\r\nA review of inclusion of baryons in chiral perturbation theory is given and \r\none-loop corrections to the Gell-Mann-Okubo relation; semileptonic hyperon decays and nonleptonic S and P wave decays are calculated. All corrections are small except the nonleptonic P wave decays and one S wave decay. The corrections to the Lee-Sugawara relation are large as a consequence of the latter.
\r\n\r\nSome predictions beyond chiral perturbation theory can be made within the soliton model of baryons. F/D ratios are predicted for hyperon magnetic moments, semileptonic decays and nonleptonic S wave decays in this model.
", "doi": "10.7907/64qa-xw17", "publication_date": "1985", "thesis_type": "phd", "thesis_year": "1985" }, { "id": "thesis:11260", "collection": "thesis", "collection_id": "11260", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10312018-091543048", "type": "thesis", "title": "Monte-Carlo Renormalisation Group for Lattice QCD", "author": [ { "family_name": "Patel", "given_name": "Apoorva Dayaram", "orcid": "0000-0002-9021-9051", "clpid": "Patel-Apoorva-Dayaram" } ], "thesis_advisor": [ { "family_name": "Fox", "given_name": "Geoffrey C.", "clpid": "Fox-G-C" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Feynman", "given_name": "Richard Phillips", "clpid": "Feynman-R-P" }, { "family_name": "Porter", "given_name": "Frank C.", "orcid": "0000-0003-1948-8889", "clpid": "Porter-F-C" }, { "family_name": "Fox", "given_name": "Geoffrey C.", "clpid": "Fox-G-C" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "The properties of the SU(2) and SU(3) lattice gauge theories are investigated using the Real Space Monte-Carlo Renormalisation Group method. The \"\u221a3 block transformation\" is found to be very efficient in this analysis. The non-perturbative \u03b2-function is calculated for the SU(2) lattice gauge theory over a large range of couplings and along both the Wilson axis and the Migdal-Kadanoff improved action line. A possible explanation of the observed nonperturbative features of the \u03b2-function is given. The same data sample is used to calculate the improved action needed for better numerical simulations, and the results are compared with those obtained using the Migdal-Kadanoff approximate renormalisation and Symanzik's perturbative improvement approach. A similar but less extensive analysis is done for the SU(3) lattice gauge theory as well.
\r\n\r\nThe results indicate that even for the pure gauge theory, the present day Monte-Carlo calculations are far from establishing an agreement with the expected asymptotic scaling. However, an improved action approach, combined with the \u03b2-function determined using the Monte-Carlo Renormalisation Group technique, should make it possible to convincingly demonstrate the scaling behaviour in near future.
", "doi": "10.7907/m791-na19", "publication_date": "1984", "thesis_type": "phd", "thesis_year": "1984" } ]