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B." } }, { "name": { "family": "Roushan", "given": "P." }, "orcid": "0000-0003-1917-3879" } ] }, "title": "Formation of robust bound states of interacting microwave photons", "ispublished": "pub", "full_text_status": "public", "keywords": "Multidisciplinary", "note": "\u00a9 The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. \n\nContributions. A. Morvan, C.N., I.A., L.B.I. and P.R. designed the experiment. A. Morvan and T.I.A. performed the experiment and analysed the data and wrote the supplement. K.K., D.A.A., I.A. and L.B.I. provided theoretical support and analysis. A. Morvan, T.A., X.M., C.N. and A.P. developed the calibration of the fSim gate. D.A.A. and A. Michailidis performed numerical simulation in the supplements. A. Morvan, T.A., I.A., L.B. and P.R. wrote the manuscript. All authors contributed to revising the manuscript and the Supplementary Information. All authors contributed to the experimental and theoretical infrastructure to enable the experiment. \n\nData availability. The datasets generated and analysed for this study are available at https://doi.org/10.5281/zenodo.6981407. \n\nThe authors declare no competing interests.\n\n
Published - s41586-022-05348-y.pdf
Supplemental Material - 41586_2022_5348_MOESM1_ESM.pdf
", "abstract": "Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-\u00bd XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.", "date": "2022-12-08", "date_type": "published", "publication": "Nature", "volume": "612", "number": "7939", "publisher": "Nature Publishing Group", "pagerange": "240-245", "id_number": "CaltechAUTHORS:20230314-845402300.28", "issn": "0028-0836", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230314-845402300.28", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "IQIM" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1038/s41586-022-05348-y", "pmcid": "PMC9729104", "primary_object": { "basename": "41586_2022_5348_MOESM1_ESM.pdf", "url": "https://authors.library.caltech.edu/records/1xqr6-fsg75/files/41586_2022_5348_MOESM1_ESM.pdf" }, "related_objects": [ { "basename": "s41586-022-05348-y.pdf", "url": "https://authors.library.caltech.edu/records/1xqr6-fsg75/files/s41586-022-05348-y.pdf" } ], "resource_type": "article", "pub_year": "2022", "author_list": "Morvan, A.; Andersen, T. 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J." } }, { "name": { "family": "Shvarts", "given": "V." } }, { "name": { "family": "Strain", "given": "D." } }, { "name": { "family": "Su", "given": "Y." } }, { "name": { "family": "Szalay", "given": "M." }, "orcid": "0000-0002-1310-9174" }, { "name": { "family": "Vidal", "given": "G." } }, { "name": { "family": "Villalonga", "given": "B." } }, { "name": { "family": "Vollgraff-Heidweiller", "given": "C." }, "orcid": "0000-0002-6513-9885" }, { "name": { "family": "White", "given": "T." }, "orcid": "0000-0002-9803-7471" }, { "name": { "family": "Yao", "given": "Z." }, "orcid": "0000-0003-1806-5454" }, { "name": { "family": "Yeh", "given": "P." }, "orcid": "0000-0003-0837-1028" }, { "name": { "family": "Yoo", "given": "J." } }, { "name": { "family": "Zalcman", "given": "A." }, "orcid": "0000-0002-2585-2424" }, { "name": { "family": "Zhang", "given": "Y." } }, { "name": { "family": "Zhu", "given": "N." }, "orcid": "0000-0002-3037-2003" }, { "name": { "family": "Neven", "given": "H." }, "orcid": "0000-0002-9681-6746" }, { "name": { "family": "Bacon", "given": "D." }, "orcid": "0000-0001-6266-9269" }, { "name": { "family": "Hilton", "given": "J." } }, { "name": { "family": "Lucero", "given": "E." }, "orcid": "0000-0002-6449-2273" }, { "name": { "family": "Babbush", "given": "R." }, "orcid": "0000-0001-6979-9533" }, { "name": { "family": "Boixo", "given": "S." }, "orcid": "0000-0002-1090-7584" }, { "name": { "family": "Megrant", "given": "A." }, "orcid": "0000-0002-6371-6140" }, { "name": { "family": "Chen", "given": "Y." }, "orcid": "0000-0002-7473-6745" }, { "name": { "family": "Kelly", "given": "J." }, "orcid": "0000-0002-2596-2121" }, { "name": { "family": "Smelyanskiy", "given": "V." }, "orcid": "0000-0002-3000-6732" }, { "name": { "family": "Abanin", "given": "D. A." }, "orcid": "0000-0002-2461-0271" }, { "name": { "family": "Roushan", "given": "P." }, "orcid": "0000-0003-1917-3879" } ] }, "title": "Noise-resilient edge modes on a chain of superconducting qubits", "ispublished": "pub", "full_text_status": "public", "keywords": "Multidisciplinary", "note": "\u00a9 2022 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. \n\nWe have benefited from discussions with M. H. Devoret, L. G. Dias, I. K. Drozdov, P. Ghaemi, and A. Rahmani. \n\nD.B. is a CIFAR Associate Fellow in the Quantum Information Science Program. \n\nAuthor contributions: D.A.A. and V.Sm. conceived of the project. X.M., D.A.A., and V.Sm. designed the experiment. X.M. executed the experiment. P.R., X.M., D.A.A., M.So., and M.Y.N. performed analysis of the experimental results. K.W.L. and B.F. contributed to measurements in the supplementary materials. X.M., P.R., and D.A.A. wrote the manuscript. V.Sm. and P.R. led and coordinated the project. Infrastructure support was provided by Google Quantum AI. All authors contributed to revising the manuscript and the supplementary materials. \n\nData and materials availability: Experimental data shown in the main text and supplementary materials, as well as simulation software code, are available in Zenodo (46). \n\nThe authors declare no competing interests.", "abstract": "Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model, which exhibits nonlocal Majorana edge modes (MEMs) with \u2124\u2082 parity symmetry. We find that any multiqubit Pauli operator overlapping with the MEMs exhibits a uniform late-time decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This characteristic allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Furthermore, the MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism. Our work elucidates the complex interplay between noise and symmetry-protected edge modes in a solid-state environment.", "date": "2022-11-18", "date_type": "published", "publication": "Science", "volume": "378", "number": "6621", "publisher": "American Association for the Advancement of Science", "pagerange": "785-790", "id_number": "CaltechAUTHORS:20230725-746101000.26", "issn": "0036-8075", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230725-746101000.26", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Canadian Institute for Advanced Research (CIFAR)" } ] }, "doi": "10.1126/science.abq5769", "resource_type": "article", "pub_year": "2022", "author_list": "Mi, X.; Sonner, M.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dzqj3-58221", "eprint_id": 114017, "eprint_status": "archive", "datestamp": "2023-08-22 14:21:58", "lastmod": "2023-10-23 18:00:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gu-Yingfei", "name": { "family": "Gu", "given": "Yingfei" }, "orcid": "0000-0001-8645-879X" }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Zhang-Pengfei-PHYSICS", "name": { "family": "Zhang", "given": "Pengfei" }, "orcid": "0000-0002-7408-0918" } ] }, "title": "A two-way approach to out-of-time-order correlators", "ispublished": "pub", "full_text_status": "public", "keywords": "1/N Expansion; Field Theories in Lower Dimensions; AdS-CFT Correspondence; Nuclear and High Energy Physics", "note": "\u00a9 2022 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived 01 December 2021. Accepted 01 March 2022. Published 21 March 2022. \n\nWe thank Douglas Stanford and Juan Maldacena for useful comments. Yingfei Gu and Pengfei Zhang also thank Shunyu Yao for explaining the paper [22] to them. Yingfei Gu is supported by the Simons Foundation through the \"It from Qubit\" program. Alexei Kitaev is supported by the Simons Foundation under grant 376205 and through the \"It from Qubit\" program, as well as by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation. Pengfei Zhang acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech.\n\nPublished - Gu2022_Article_ATwo-wayApproachToOut-of-time-.pdf
Accepted Version - 2111.12007.pdf
", "abstract": "Out-of-time-order correlators (OTOCs) are a standard measure of quantum chaos. Of the four operators involved, one pair may be regarded as a source and the other as a probe. A usual approach, applicable to large-N systems such as the SYK model, is to replace the actual source with some mean-field perturbation and solve for the probe correlation function on the double Keldysh contour. We show how to obtain the OTOC by combining two such solutions for perturbations propagating forward and backward in time. These dynamical perturbations, or scrambling modes, are considered on the thermofield double background and decomposed into a coherent and an incoherent part. For the large-q SYK, we obtain the OTOC in a closed form. We also prove a previously conjectured relation between the Lyapunov exponent and high-frequency behavior of the spectral function.", "date": "2022-03", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2022", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 133", "id_number": "CaltechAUTHORS:20220323-545297000", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220323-545297000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/jhep03(2022)133", "primary_object": { "basename": "2111.12007.pdf", "url": "https://authors.library.caltech.edu/records/dzqj3-58221/files/2111.12007.pdf" }, "related_objects": [ { "basename": "Gu2022_Article_ATwo-wayApproachToOut-of-time-.pdf", "url": "https://authors.library.caltech.edu/records/dzqj3-58221/files/Gu2022_Article_ATwo-wayApproachToOut-of-time-.pdf" } ], "resource_type": "article", "pub_year": "2022", "author_list": "Gu, Yingfei; Kitaev, Alexei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2sbj7-6dx61", "eprint_id": 111675, "eprint_status": "archive", "datestamp": "2023-08-20 06:19:48", "lastmod": "2023-10-23 15:33:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mi-Xiao", "name": { "family": "Mi", "given": "Xiao" }, "orcid": "0000-0003-0507-0211" }, { "name": { "family": "Roushan", "given": "Pedram" }, "orcid": "0000-0003-1917-3879" }, { "name": { "family": "Quintana", "given": "Chris" }, "orcid": "0000-0003-4408-8318" }, { "name": { "family": "Mandr\u00e0", "given": "Salvatore" }, "orcid": "0000-0002-3908-2694" }, { "name": { "family": "Marshall", "given": "Jeffrey" }, "orcid": "0000-0002-5011-1281" }, { "name": { "family": "Neill", "given": "Charles" }, "orcid": "0000-0002-6563-3568" }, { "name": { "family": "Arute", "given": "Frank" } }, { "name": { "family": "Arya", "given": "Kunal" }, "orcid": "0000-0002-6486-7100" }, { "name": { "family": "Atalaya", "given": "Juan" }, "orcid": "0000-0003-3055-2730" }, { "name": { "family": "Babbush", "given": "Ryan" }, "orcid": "0000-0001-6979-9533" }, { "name": { "family": "Bardin", "given": "Joseph C." }, "orcid": "0000-0002-6523-6730" }, { "name": { "family": "Barends", "given": "Rami" } }, { "name": { "family": "Basso", "given": "Joao" }, "orcid": "0000-0001-5547-691X" }, { "name": { "family": "Bengtsson", "given": "Andreas" }, "orcid": "0000-0001-5264-4025" }, { "name": { "family": "Boixo", "given": "Sergio" }, "orcid": "0000-0002-1090-7584" }, { "name": { "family": "Bourassa", "given": "Alexandre" }, "orcid": "0000-0002-8517-7475" }, { "name": { "family": "Broughton", "given": "Michael" } }, { "name": { "family": "Buckley", "given": "Bob B." }, "orcid": "0000-0001-5139-7931" }, { "name": { "family": "Buell", "given": "David A." } }, { "name": { "family": "Burkett", "given": "Brian" }, "orcid": "0000-0001-8474-6317" }, { "name": { "family": "Bushnell", "given": "Nicholas" }, "orcid": "0000-0001-7445-1654" }, { "name": { "family": "Chen", "given": "Zijun" } }, { "name": { "family": "Chiaro", "given": "Benjamin" }, "orcid": "0000-0002-2913-2790" }, { "name": { "family": "Collins", "given": "Roberto" }, "orcid": "0000-0002-6164-0007" }, { "name": { "family": "Courtney", "given": "William" } }, { "name": { "family": "Demura", "given": "Sean" }, "orcid": "0000-0003-3727-7380" }, { "name": { "family": "Derk", "given": "Alan R." } }, { "name": { "family": "Dunsworth", "given": "Andrew" } }, { "name": { "family": "Eppens", "given": "Daniel" }, "orcid": "0000-0001-7134-5733" }, { "name": { "family": "Erickson", "given": "Catherine" } }, { "name": { "family": "Farhi", "given": "Edward" } }, { "name": { "family": "Fowler", "given": "Austin G." }, "orcid": "0000-0002-9048-2896" }, { "name": { "family": "Foxen", "given": "Brooks" }, "orcid": "0000-0002-3732-168X" }, { "name": { "family": "Gidney", "given": "Craig" } }, { "name": { "family": "Giustina", "given": "Marissa" } }, { "name": { "family": "Gross", "given": "Jonathan A." }, "orcid": "0000-0001-7049-6206" }, { "name": { "family": "Harrigan", "given": "Matthew P." }, "orcid": "0000-0001-9412-0553" }, { "name": { "family": "Harrington", "given": "Sean D." }, "orcid": "0000-0003-0521-8378" }, { "name": { "family": "Hilton", "given": "Jeremy" } }, { "name": { "family": "Ho", "given": "Alan" } }, { "name": { "family": "Hong", "given": "Sabrina" } }, { "name": { "family": "Huang", "given": "Trent" } }, { "name": { "family": "Huggins", "given": "William J." }, "orcid": "0000-0003-2735-1380" }, { "name": { "family": "Ioffe", "given": "L. B." }, "orcid": "0000-0002-8777-6789" }, { "name": { "family": "Isakov", "given": "Sergei V." } }, { "name": { "family": "Jeffrey", "given": "Evan" } }, { "name": { "family": "Jiang", "given": "Zhang" }, "orcid": "0000-0003-0435-655X" }, { "name": { "family": "Jones", "given": "Cody" } }, { "name": { "family": "Kafri", "given": "Dvir" }, "orcid": "0000-0001-9160-5176" }, { "name": { "family": "Kelly", "given": "Julian" }, "orcid": "0000-0002-2596-2121" }, { "name": { "family": "Kim", "given": "Seon" }, "orcid": "0000-0003-3397-0444" }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "name": { "family": "Klimov", "given": "Paul V." } }, { "name": { "family": "Korotkov", "given": "Alexander N." } }, { "name": { "family": "Kostritsa", "given": "Fedor" } }, { "name": { "family": "Landhuis", "given": "David" }, "orcid": "0000-0001-9804-2185" }, { "name": { "family": "Laptev", "given": "Pavel" } }, { "name": { "family": "Lucero", "given": "Erik" }, "orcid": "0000-0002-6449-2273" }, { "name": { "family": "Martin", "given": "Orion" }, "orcid": "0000-0002-9576-573X" }, { "name": { "family": "McClean", "given": "Jarrod R." }, "orcid": "0000-0002-2809-0509" }, { "name": { "family": "McCourt", "given": "Trevor" } }, { "name": { "family": "McEwen", "given": "Matt" }, "orcid": "0000-0002-9544-141X" }, { "name": { "family": "Megrant", "given": "Anthony" }, "orcid": "0000-0002-6371-6140" }, { "name": { "family": "Miao", "given": "Kevin C." } }, { "name": { "family": "Mohseni", "given": "Masoud" } }, { "name": { "family": "Montazeri", "given": "Shirin" } }, { "name": { "family": "Mruczkiewicz", "given": "Wojciech" }, "orcid": "0000-0002-8497-6363" }, { "name": { "family": "Mutus", "given": "Josh" } }, { "name": { "family": "Naaman", "given": "Ofer" }, "orcid": "0000-0002-7760-9186" }, { "name": { "family": "Neeley", "given": "Matthew" }, "orcid": "0000-0002-5548-0051" }, { "name": { "family": "Newman", "given": "Michael" } }, { "name": { "family": "Niu", "given": "Murphy Yuezhen" } }, { "name": { "family": "O'Brien", "given": "Thomas E." }, "orcid": "0000-0002-8406-6626" }, { "name": { "family": "Opremcak", "given": "Alex" } }, { "name": { "family": "Ostby", "given": "Eric" } }, { "name": { "family": "Pato", "given": "Balint" } }, { "name": { "family": "Petukhov", "given": "Andre" } }, { "name": { "family": "Redd", "given": "Nicholas" }, "orcid": "0000-0002-6549-5441" }, { "name": { "family": "Rubin", "given": "Nicholas C." }, "orcid": "0000-0003-3963-1830" }, { "name": { "family": "Sank", "given": "Daniel" }, "orcid": "0000-0001-8188-364X" }, { "name": { "family": "Satzinger", "given": "Kevin J." }, "orcid": "0000-0001-5865-0813" }, { "name": { "family": "Shvarts", "given": "Vladimir" } }, { "name": { "family": "Strain", "given": "Doug" } }, { "name": { "family": "Szalay", "given": "Marco" }, "orcid": "0000-0002-1310-9174" }, { "name": { "family": "Trevithick", "given": "Matthew D." }, "orcid": "0000-0001-6700-3140" }, { "name": { "family": "Villalonga", "given": "Benjamin" } }, { "name": { "family": "White", "given": "Theodore" }, "orcid": "0000-0002-9803-7471" }, { "name": { "family": "Yao", "given": "Z. Jamie" }, "orcid": "0000-0003-1806-5454" }, { "name": { "family": "Yeh", "given": "Ping" }, "orcid": "0000-0003-0837-1028" }, { "name": { "family": "Zalcman", "given": "Adam" }, "orcid": "0000-0002-2585-2424" }, { "name": { "family": "Neven", "given": "Hartmut" }, "orcid": "0000-0002-9681-6746" }, { "name": { "family": "Aleiner", "given": "Igor" } }, { "name": { "family": "Kechedzhi", "given": "Kostyantyn" }, "orcid": "0000-0002-0136-1428" }, { "name": { "family": "Smelyanskiy", "given": "Vadim" }, "orcid": "0000-0002-3000-6732" }, { "name": { "family": "Chen", "given": "Yu" }, "orcid": "0000-0002-7473-6745" } ] }, "title": "Information scrambling in quantum circuits", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 American Association for the Advancement of Science. \n\nReceived 9 January 2021; accepted 19 October 2021. Published online 28 October 2021. \n\nP.R. and X.M. acknowledge fruitful discussions with P. Zoller, B. Vermersch, A. Elben, and M. Knapp. \n\nS.Ma. and J.Ma. acknowledge support from the NASA Ames Research Center and support from the NASA Advanced Supercomputing Division for providing access to the NASA HPC systems, Pleiades and Merope. S.Ma. and J.Ma. also acknowledge support from the AFRL Information Directorate under grant no. F4HBKC4162G001. J.Ma. is partially supported by NAMS contract no. NNA16BD14C. S.Ma. is also supported by the Prime contract no. 80ARC020D0010 with the NASA Ames Research Center. \n\nAuthor contributions: V.Sm., K.K., X.M., and P.R. devised the experiment. X.M., C.Q., and P.R. executed the experiment on the Google quantum hardware. X.M., P.R., K.K., and Y.C. wrote the manuscript. X.M., S.Ma., J.Ma., and K.K. wrote the supplementary materials. V.Sm., I.A., X.M., K.K., S.Ma., and J.Ma. provided theoretical support, analysis techniques, and numerical computations. I.A. and K.K. developed the Markov process model. S.Ma. designed and performed the large-scale numerical simulation, including the algorithms and software development. J.Ma. performed the noisy numerical simulations. P.R., Y.C., V.Sm., and H.N. led and coordinated the project. Infrastructure support was provided by the Google Quantum AI hardware team. The NASA Advanced Supercomputing Division at NASA Ames provided the infrastructure to run high-performance computing (HPC) simulations. All authors contributed to revising the manuscript and the supplementary materials. \n\nThe authors declare no competing interest. \n\nData and materials availability: All experimental and numerical data in the main text and supplementary materials, along with the software code for generating quantum circuits, measurements, population dynamics simulation, and tensor contraction simulation are available at Zenodo (43).\n\nSubmitted - 2101.08870.pdf
Supplemental Material - science.abg5029_sm.pdf
", "abstract": "Interactions in quantum systems can spread initially localized quantum information into the exponentially many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is key to resolving several open questions in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish operator spreading and operator entanglement and experimentally observe their respective signatures. We show that whereas operator spreading is captured by an efficient classical model, operator entanglement in idealized circuits requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors.", "date": "2021-12-17", "date_type": "published", "publication": "Science", "volume": "374", "number": "6574", "publisher": "American Association for the Advancement of Science", "pagerange": "1479-1483", "id_number": "CaltechAUTHORS:20211028-210102101", "issn": "0036-8075", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211028-210102101", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Research Laboratory (AFRL)", "grant_number": "F4HBKC4162G001" }, { "agency": "NASA", "grant_number": "NNA16BD14C" }, { "agency": "NASA", "grant_number": "80ARC020D0010" } ] }, "local_group": { "items": [ { "id": "IQIM" } ] }, "doi": "10.1126/science.abg5029", "primary_object": { "basename": "2101.08870.pdf", "url": "https://authors.library.caltech.edu/records/2sbj7-6dx61/files/2101.08870.pdf" }, "related_objects": [ { "basename": "science.abg5029_sm.pdf", "url": "https://authors.library.caltech.edu/records/2sbj7-6dx61/files/science.abg5029_sm.pdf" } ], "resource_type": "article", "pub_year": "2021", "author_list": "Mi, Xiao; Roushan, Pedram; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/a1g0e-36b86", "eprint_id": 112190, "eprint_status": "archive", "datestamp": "2023-08-22 12:43:02", "lastmod": "2023-10-23 20:57:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Satzinger-Kevin-J", "name": { "family": "Satzinger", "given": "K. J." }, "orcid": "0000-0001-5865-0813" }, { "name": { "family": "Liu", "given": "Y.-J" }, "orcid": "0000-0002-7657-9464" }, { "name": { "family": "Smith", "given": "A." }, "orcid": "0000-0002-6744-4592" }, { "id": "Knapp-Christina", "name": { "family": "Knapp", "given": "C." }, "orcid": "0000-0002-5982-8107" }, { "name": { "family": "Newman", "given": "M." } }, { "name": { "family": "Jones", "given": "C." } }, { "name": { "family": "Chen", "given": "Z." } }, { "name": { "family": "Quintana", "given": "C." } }, { "name": { "family": "Mi", "given": "X." }, "orcid": "0000-0003-0507-0211" }, { "name": { "family": "Dunsworth", "given": "A." } }, { "name": { "family": "Gidney", "given": "C." } }, { "name": { "family": "Aleiner", "given": "I." } }, { "name": { "family": "Arute", "given": "F." } }, { "name": { "family": "Arya", "given": "K." }, "orcid": "0000-0002-6486-7100" }, { "name": { "family": "Atalaya", "given": "J." } }, { "name": { "family": "Babbush", "given": "R." }, "orcid": "0000-0001-6979-9533" }, { "name": { "family": "Bardin", "given": "J. C." }, "orcid": "0000-0002-6523-6730" }, { "name": { "family": "Barends", "given": "R." } }, { "name": { "family": "Basso", "given": "J." }, "orcid": "0000-0001-5547-691X" }, { "name": { "family": "Bengtsson", "given": "A." }, "orcid": "0000-0001-5264-4025" }, { "name": { "family": "Bilmes", "given": "A." } }, { "name": { "family": "Broughton", "given": "M." } }, { "name": { "family": "Buckley", "given": "B. B." }, "orcid": "0000-0001-5139-7931" }, { "name": { "family": "Buell", "given": "D. A." } }, { "name": { "family": "Burkett", "given": "B." }, "orcid": "0000-0001-8474-6317" }, { "name": { "family": "Bushnell", "given": "N." }, "orcid": "0000-0001-7445-1654" }, { "name": { "family": "Chiaro", "given": "B." } }, { "name": { "family": "Collins", "given": "R." }, "orcid": "0000-0002-6164-0007" }, { "name": { "family": "Courtney", "given": "W." } }, { "name": { "family": "Demura", "given": "S." }, "orcid": "0000-0003-3727-7380" }, { "name": { "family": "Derk", "given": "A. R." } }, { "name": { "family": "Eppens", "given": "D." }, "orcid": "0000-0001-7134-5733" }, { "name": { "family": "Erickson", "given": "C." } }, { "name": { "family": "Faoro", "given": "L." } }, { "name": { "family": "Farhi", "given": "E." } }, { "name": { "family": "Fowler", "given": "A. G." }, "orcid": "0000-0002-9048-2896" }, { "name": { "family": "Foxen", "given": "B." }, "orcid": "0000-0002-3732-168X" }, { "name": { "family": "Giustina", "given": "M." } }, { "name": { "family": "Greene", "given": "A." }, "orcid": "0000-0002-4034-8744" }, { "name": { "family": "Gross", "given": "J. A." }, "orcid": "0000-0001-7049-6206" }, { "name": { "family": "Harrigan", "given": "M. P." }, "orcid": "0000-0001-9412-0553" }, { "name": { "family": "Harrington", "given": "S. D." }, "orcid": "0000-0003-0521-8378" }, { "name": { "family": "Hilton", "given": "J." } }, { "name": { "family": "Hong", "given": "S." } }, { "name": { "family": "Huang", "given": "T." } }, { "name": { "family": "Huggins", "given": "W. J." } }, { "name": { "family": "Ioffe", "given": "L. B." }, "orcid": "0000-0002-8777-6789" }, { "name": { "family": "Isakov", "given": "S. V." } }, { "name": { "family": "Jeffrey", "given": "E." } }, { "name": { "family": "Jiang", "given": "Z." }, "orcid": "0000-0003-0435-655X" }, { "name": { "family": "Kafri", "given": "D." }, "orcid": "0000-0001-9160-5176" }, { "name": { "family": "Kechedzhi", "given": "K." }, "orcid": "0000-0002-0136-1428" }, { "name": { "family": "Khattar", "given": "T." } }, { "name": { "family": "Kim", "given": "S." }, "orcid": "0000-0003-3397-0444" }, { "name": { "family": "Klimov", "given": "P. V." } }, { "name": { "family": "Korotkov", "given": "A. N." } }, { "name": { "family": "Kostritsa", "given": "F." } }, { "name": { "family": "Landhuis", "given": "D." }, "orcid": "0000-0001-9804-2185" }, { "name": { "family": "Laptev", "given": "P." } }, { "name": { "family": "Locharla", "given": "A." } }, { "name": { "family": "Lucero", "given": "E." }, "orcid": "0000-0002-6449-2273" }, { "name": { "family": "Martin", "given": "O." }, "orcid": "0000-0002-9576-573X" }, { "name": { "family": "McClean", "given": "J. R." }, "orcid": "0000-0002-2809-0509" }, { "name": { "family": "McEwen", "given": "M." }, "orcid": "0000-0002-9544-141X" }, { "name": { "family": "Miao", "given": "K. C." } }, { "name": { "family": "Mohseni", "given": "M." } }, { "name": { "family": "Montazeri", "given": "S." } }, { "name": { "family": "Mruczkiewicz", "given": "W." }, "orcid": "0000-0002-8497-6363" }, { "name": { "family": "Mutus", "given": "J." } }, { "name": { "family": "Naaman", "given": "O." }, "orcid": "0000-0002-7760-9186" }, { "name": { "family": "Neeley", "given": "M." }, "orcid": "0000-0002-5548-0051" }, { "name": { "family": "Neill", "given": "C." }, "orcid": "0000-0002-6563-3568" }, { "name": { "family": "Niu", "given": "M. Y." } }, { "name": { "family": "O'Brien", "given": "T. E." }, "orcid": "0000-0002-8406-6626" }, { "name": { "family": "Opremcak", "given": "A." } }, { "name": { "family": "Pat\u00f3", "given": "B." } }, { "name": { "family": "Petukhov", "given": "A." } }, { "name": { "family": "Rubin", "given": "N. C." }, "orcid": "0000-0003-3963-1830" }, { "name": { "family": "Sank", "given": "D." }, "orcid": "0000-0001-8188-364X" }, { "name": { "family": "Shvarts", "given": "V." } }, { "name": { "family": "Strain", "given": "D." } }, { "name": { "family": "Szalay", "given": "M." }, "orcid": "0000-0002-1310-9174" }, { "name": { "family": "Villalonga", "given": "B." } }, { "name": { "family": "White", "given": "T. C." }, "orcid": "0000-0002-9803-7471" }, { "name": { "family": "Yao", "given": "Z." }, "orcid": "0000-0003-1806-5454" }, { "name": { "family": "Yeh", "given": "P." }, "orcid": "0000-0003-0837-1028" }, { "name": { "family": "Yoo", "given": "J." } }, { "name": { "family": "Zalcman", "given": "A." }, "orcid": "0000-0002-2585-2424" }, { "name": { "family": "Neven", "given": "H." }, "orcid": "0000-0002-9681-6746" }, { "name": { "family": "Boixo", "given": "S." }, "orcid": "0000-0002-1090-7584" }, { "name": { "family": "Megrant", "given": "A." }, "orcid": "0000-0002-6371-6140" }, { "name": { "family": "Chen", "given": "Y." }, "orcid": "0000-0002-7473-6745" }, { "name": { "family": "Kelly", "given": "J." } }, { "name": { "family": "Smelyanskiy", "given": "V." }, "orcid": "0000-0002-3000-6732" }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A." }, "orcid": "0000-0002-5777-642X" }, { "name": { "family": "Knap", "given": "M." }, "orcid": "0000-0002-7093-9502" }, { "name": { "family": "Pollmann", "given": "F." }, "orcid": "0000-0003-0320-9304" }, { "name": { "family": "Roushan", "given": "P." }, "orcid": "0000-0003-1917-3879" } ] }, "title": "Realizing topologically ordered states on a quantum processor", "ispublished": "pub", "full_text_status": "public", "keywords": "Multidisciplinary", "note": "\u00a9 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. https://www.sciencemag.org/about/science-licenses-journal-article-reuse This is an article distributed under the terms of the Science Journals Default License. \n\n2 April 2021; accepted 28 October 2021. \n\nWe thank B. Bauer, A. Elben, B. Vermersch, and G. Vidal for useful discussions. \n\nF.P., Y.-J.L., A.S., and M.K. acknowledge support from the Technical University of Munich\u2013Institute for Advanced Study, funded by the German Excellence Initiative and the European Union FP7 under grant agreement 291763; the Max Planck Gesellschaft (MPG) through the International Max Planck Research School for Quantum Science and Technology (IMPRS-QST); the Deutsche Forschungsgemeinschaft (DFG; German Research Foundation) under Germany's Excellence Strategy\u2013EXC\u20132111\u2013390814868, TRR80, and DFG grant KN1254/2-1; and from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreements 771537 and 851161). A.S. was supported by a Research Fellowship from the Royal Commission for the Exhibition of 1851. C.K. was supported by the Walter Burke Institute for Theoretical Physics at Caltech, and by the IQIM, an NSF Frontier center funded by the Gordon and Betty Moore Foundation, the Packard Foundation, and the Simons Foundation. \n\nAuthor contributions: A.S., M.K., F.P., K.J.S., Y.-J.L., C.K., and P.R. designed the experiment. K.J.S. and P.R. performed the experiment. K.J.S. and Y.-J.L. analyzed the data and wrote the supplement. Y.-J.L., A.S., C.K., M.K., F.P., and K.J.S. provided theoretical support and analysis. C.K., K.JS., Y.-J.L., A.S., M.K., F.P., and P.R. wrote the manuscript. All authors contributed to revising the manuscript and supplement. All authors contributed to the experimental and theoretical infrastructure to enable the experiment. \n\nThe authors declare no competing interests. \n\nData and materials availability: Data and code used for analysis and simulation are available at (44).\n\nSubmitted - 2104.01180.pdf
Supplemental Material - science.abi8378_sm.pdf
", "abstract": "The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error\u2013correcting codes. Realizing topologically ordered states has proven to be challenging in both condensed matter and synthetic quantum systems. We prepared the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measured a topological entanglement entropy near the expected value of \u2013ln2 and simulated anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigated key aspects of the surface code, including logical state injection and the decay of the nonlocal order parameter. Our results demonstrate the potential for quantum processors to provide insights into topological quantum matter and quantum error correction.", "date": "2021-12-03", "date_type": "published", "publication": "Science", "volume": "374", "number": "6572", "publisher": "American Association for the Advancement of Science", "pagerange": "1237-1241", "id_number": "CaltechAUTHORS:20211203-174950058", "issn": "0036-8075", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211203-174950058", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Technical University of Munich" }, { "agency": "European Research Council (ERC)", "grant_number": "291763" }, { "agency": "International Max Planck Research School for Quantum Science and Technology" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111-390814868" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "TRR80" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "KN1254/2-1" }, { "agency": "European Research Council (ERC)", "grant_number": "771537" }, { "agency": "European Research Council (ERC)", "grant_number": "851161" }, { "agency": "Royal Commission for the Exhibition of 1851" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "NSF" }, { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1126/science.abi8378", "primary_object": { "basename": "science.abi8378_sm.pdf", "url": "https://authors.library.caltech.edu/records/a1g0e-36b86/files/science.abi8378_sm.pdf" }, "related_objects": [ { "basename": "2104.01180.pdf", "url": "https://authors.library.caltech.edu/records/a1g0e-36b86/files/2104.01180.pdf" } ], "resource_type": "article", "pub_year": "2021", "author_list": "Satzinger, K. J.; Liu, Y.-J; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/akebf-7dn96", "eprint_id": 110054, "eprint_status": "archive", "datestamp": "2023-08-22 10:33:58", "lastmod": "2023-10-23 18:16:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chen-Zijun", "name": { "family": "Chen", "given": "Zijun" } }, { "name": { "family": "Satzinger", "given": "Kevin J." } }, { "name": { "family": "Atalaya", "given": "Juan" } }, { "name": { "family": "Korotkov", "given": "Alexander N." } }, { "name": { "family": "Dunsworth", "given": "Andrew" } }, { "name": { "family": "Sank", "given": "Daniel" } }, { "name": { "family": "Quintana", "given": "Chris" } }, { "name": { "family": "McEwen", "given": "Matt" }, "orcid": "0000-0002-9544-141X" }, { "name": { "family": "Barends", "given": "Rami" } }, { "name": { "family": "Klimov", "given": "Paul V." } }, { "name": { "family": "Hong", "given": "Sabrina" } }, { "name": { "family": "Jones", "given": "Cody" } }, { "name": { "family": "Petukhov", "given": "Andre" } }, { "name": { "family": "Kafri", "given": "Dvir" } }, { "name": { "family": "Demura", "given": "Sean" }, "orcid": "0000-0003-3727-7380" }, { "name": { "family": "Burkett", "given": "Brian" }, "orcid": "0000-0001-8474-6317" }, { "name": { "family": "Gidney", "given": "Craig" } }, { "name": { "family": "Fowler", "given": "Austin G." } }, { "name": { "family": "Paler", "given": "Alexandru" }, "orcid": "0000-0002-1536-8858" }, { "id": "Putterman-Harald", "name": { "family": "Putterman", "given": "Harald" } }, { "name": { "family": "Aleiner", "given": "Igor" } }, { "name": { "family": "Arute", "given": "Frank" } }, { "name": { "family": "Arya", "given": "Kunal" } }, { "name": { "family": "Babbush", "given": "Ryan" } }, { "name": { "family": "Bardin", "given": "Joseph C." }, "orcid": "0000-0002-6523-6730" }, { "name": { "family": "Bengtsson", "given": "Andreas" } }, { "name": { "family": "Bourassa", "given": "Alexandre" } }, { "name": { "family": "Broughton", "given": "Michael" } }, { "name": { "family": "Buckley", "given": "Bob B." } }, { "name": { "family": "Buell", "given": "David A." } }, { "name": { "family": "Bushnell", "given": "Nicholas" } }, { "name": { "family": "Chiaro", "given": "Benjamin" } }, { "name": { "family": "Collins", "given": "Roberto" } }, { "name": { "family": "Courtney", "given": "William" } }, { "name": { "family": "Derk", "given": "Alan R." } }, { "name": { "family": "Eppens", "given": "Daniel" } }, { "name": { "family": "Erickson", "given": "Catherine" } }, { "name": { "family": "Farhi", "given": "Edward" } }, { "name": { "family": "Foxen", "given": "Brooks" } }, { "name": { "family": "Giustina", "given": "Marissa" } }, { "name": { "family": "Greene", "given": "Ami" } }, { "name": { "family": "Gross", "given": "Jonathan A." } }, { "name": { "family": "Harrigan", "given": "Matthew P." }, "orcid": "0000-0001-9412-0553" }, { "name": { "family": "Harrington", "given": "Sean D." }, "orcid": "0000-0003-0521-8378" }, { "name": { "family": "Hilton", "given": "Jeremy" } }, { "name": { "family": "Ho", "given": "Alan" } }, { "name": { "family": "Huang", "given": "Trent" } }, { "name": { "family": "Huggins", "given": "William J." }, "orcid": "0000-0003-2735-1380" }, { "name": { "family": "Ioffe", "given": "L. B." } }, { "name": { "family": "Isakov", "given": "Sergei V." } }, { "name": { "family": "Jeffrey", "given": "Evan" } }, { "name": { "family": "Jiang", "given": "Zhang" } }, { "name": { "family": "Kechedzhi", "given": "Kostyantyn" } }, { "name": { "family": "Kim", "given": "Seon" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "name": { "family": "Kostritsa", "given": "Fedor" } }, { "name": { "family": "Landhuis", "given": "David" }, "orcid": "0000-0001-9804-2185" }, { "name": { "family": "Laptev", "given": "Pavel" } }, { "name": { "family": "Lucero", "given": "Erik" } }, { "name": { "family": "Martin", "given": "Orion" } }, { "name": { "family": "McClean", "given": "Jarrod R." }, "orcid": "0000-0002-2809-0509" }, { "name": { "family": "McCourt", "given": "Trevor" } }, { "name": { "family": "Mi", "given": "Xiao" } }, { "name": { "family": "Miao", "given": "Kevin C." } }, { "name": { "family": "Mohseni", "given": "Masoud" } }, { "name": { "family": "Montazeri", "given": "Shirin" } }, { "name": { "family": "Mruczkiewicz", "given": "Wojciech" }, "orcid": "0000-0002-8497-6363" }, { "name": { "family": "Mutus", "given": "Josh" } }, { "name": { "family": "Naaman", "given": "Ofer" }, "orcid": "0000-0002-7760-9186" }, { "name": { "family": "Neeley", "given": "Matthew" }, "orcid": "0000-0002-5548-0051" }, { "name": { "family": "Neill", "given": "Charles" }, "orcid": "0000-0001-8509-9836" }, { "name": { "family": "Newman", "given": "Michael" } }, { "name": { "family": "Niu", "given": "Murphy Yuezhen" } }, { "name": { "family": "O'Brien", "given": "Thomas E." } }, { "name": { "family": "Opremcak", "given": "Alex" } }, { "name": { "family": "Ostby", "given": "Eric" } }, { "name": { "family": "Pat\u00f3", "given": "B\u00e1lint" } }, { "name": { "family": "Redd", "given": "Nicholas" }, "orcid": "0000-0002-6549-5441" }, { "name": { "family": "Roushan", "given": "Pedram" } }, { "name": { "family": "Rubin", "given": "Nicholas C." } }, { "name": { "family": "Shvarts", "given": "Vladimir" } }, { "name": { "family": "Strain", "given": "Doug" } }, { "name": { "family": "Szalay", "given": "Marco" } }, { "name": { "family": "Trevithick", "given": "Matthew D." } }, { "name": { "family": "Villalonga", "given": "Benjamin" } }, { "name": { "family": "White", "given": "Theodore" } }, { "name": { "family": "Yao", "given": "Z. Jamie" } }, { "name": { "family": "Yeh", "given": "Ping" }, "orcid": "0000-0003-0837-1028" }, { "name": { "family": "Yoo", "given": "Juhwan" } }, { "name": { "family": "Zalcman", "given": "Adam" }, "orcid": "0000-0002-2585-2424" }, { "name": { "family": "Neven", "given": "Hartmut" } }, { "name": { "family": "Boixo", "given": "Sergio" }, "orcid": "0000-0002-1090-7584" }, { "name": { "family": "Smelyanskiy", "given": "Vadim" } }, { "name": { "family": "Chen", "given": "Yu" } }, { "name": { "family": "Megrant", "given": "Anthony" }, "orcid": "0000-0002-6371-6140" }, { "name": { "family": "Kelly", "given": "Julian" }, "orcid": "0000-0002-2596-2121" } ] }, "title": "Exponential suppression of bit or phase errors with cyclic error correction", "ispublished": "pub", "full_text_status": "public", "keywords": "Quantum information; Qubits", "note": "\u00a9 The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. \n\nReceived 11 January 2021; Accepted 28 April 2021; Published 14 July 2021. \n\nWe thank J. Platt, J. Dean and J. Yagnik for their executive sponsorship of the Google Quantum AI team, and for their continued engagement and support. We thank S. Leichenauer and J. Platt for reviewing a draft of the manuscript and providing feedback. \n\nData availability: The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request. \n\nAuthor Contributions: Z.C., K.J.S., H.P., A.G.F., A.N.K. and J.K. designed the experiment. Z.C., K.J.S. and J.K. performed the experiment and analysed the data. C.Q., K.J.S., A. Petukhov and Y.C. developed the controlled-Z gate. M. McEwen, D.K., A. Petukhov and R. Barends developed the reset operation. M. McEwen and R. Barends performed experiments on leakage, reset and high-energy events in error correcting codes. D. Sank and Z.C. developed the readout operation. A.D., B.B., S.D. and A.M. led the design and fabrication of the processor. J.A. and A.N.K. developed and performed the pij analysis. C.J. developed the inverse \u039b model and performed the simulations. A.G.F. and C.G. wrote the decoder and interface software. S. H., K.J.S. and J.K. developed the dynamical decoupling protocols. P.V.K. developed error mitigation techniques based on system frequency optimization. Z.C., K.J.S., S.H., P.V.K. and J.K. developed error correction calibration techniques. Z.C., K.J.S. and J.K. wrote the manuscript. S.B., V. Smelyanskiy, Y.C., A.M. and J.K. coordinated the team-wide error correction effort. Work by H. Putterman was done prior to joining AWS. All authors contributed to revising the manuscript and writing the Supplementary Information. All authors contributed to the experimental and theoretical infrastructure to enable the experiment. \n\nThe authors declare no competing interests. \n\nPeer review information: Nature thanks Carmen Almudever, Benjamin Brown and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.\n\nPublished - s41586-021-03588-y.pdf
Supplemental Material - 41586_2021_3588_MOESM1_ESM.pdf
Supplemental Material - 41586_2021_3588_MOESM2_ESM.pdf
", "abstract": "Realizing the potential of quantum computing requires sufficiently low logical error rates(1). Many applications call for error rates as low as 10\u207b\u00b9\u2075 (refs. 2,3,4,5,6,7,8,9), but state-of-the-art quantum platforms typically have physical error rates near 10\u207b\u00b3 (refs. 10,11,12,13,14). Quantum error correction(15,16,17) promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device(18,19) and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.", "date": "2021-07-15", "date_type": "published", "publication": "Nature", "volume": "595", "number": "7867", "publisher": "Nature Publishing Group", "pagerange": "383-387", "id_number": "CaltechAUTHORS:20210728-191748877", "issn": "0028-0836", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210728-191748877", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "AWS-Center-for-Quantum-Computing" } ] }, "corp_creators": { "items": [ "Google Quantum AI" ] }, "doi": "10.1038/s41586-021-03588-y", "primary_object": { "basename": "41586_2021_3588_MOESM1_ESM.pdf", "url": "https://authors.library.caltech.edu/records/akebf-7dn96/files/41586_2021_3588_MOESM1_ESM.pdf" }, "related_objects": [ { "basename": "41586_2021_3588_MOESM2_ESM.pdf", "url": "https://authors.library.caltech.edu/records/akebf-7dn96/files/41586_2021_3588_MOESM2_ESM.pdf" }, { "basename": "s41586-021-03588-y.pdf", "url": "https://authors.library.caltech.edu/records/akebf-7dn96/files/s41586-021-03588-y.pdf" } ], "resource_type": "article", "pub_year": "2021", "author_list": "Chen, Zijun; Satzinger, Kevin J.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9fh52-1es68", "eprint_id": 108398, "eprint_status": "archive", "datestamp": "2023-08-22 09:05:51", "lastmod": "2023-10-23 17:00:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Zhang-Pengfei-PHYSICS", "name": { "family": "Zhang", "given": "Pengfei" }, "orcid": "0000-0002-7408-0918" }, { "id": "Gu-Yingfei", "name": { "family": "Gu", "given": "Yingfei" }, "orcid": "0000-0001-8645-879X" }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" } ] }, "title": "An obstacle to sub-AdS holography for SYK-like models", "ispublished": "pub", "full_text_status": "public", "keywords": "1/N Expansion; AdS-CFT Correspondence", "note": "\u00a9 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: December 16, 2020; Revised: January 22, 2021; Accepted: January 28, 2021; Published: March 9, 2021. \n\nWe acknowledge Hui Zhai for collaboration in the early stages of this project. We thank Douglas Stanford for helpful discussions. Y.G. is supported by the Gordon and Betty Moore Foundation EPiQS Initiative through Grant (GBMF-4306), and by the Simons Foundation through the \"It from Qubit\" program\". A.K. is supported by the Simons Foundation under grant 376205 and through the \"It from Qubit\" program, as well as by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation. P.Z. acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech.\n\nPublished - Zhang2021_Article_AnObstacleToSub-AdSHolographyF.pdf
Submitted - 2012.01620.pdf
", "abstract": "We argue that \"stringy\" effects in a putative gravity-dual picture for SYK-like models are related to the branching time, a kinetic coefficient defined in terms of the retarded kernel. A bound on the branching time is established assuming that the leading diagrams are ladders with thin rungs. Thus, such models are unlikely candidates for sub-AdS holography. In the weak coupling limit, we derive a relation between the branching time, the Lyapunov exponent, and the quasiparticle lifetime using two different approximations.", "date": "2021-03", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2021", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 94", "id_number": "CaltechAUTHORS:20210311-125528811", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210311-125528811", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Gordon and Betty Moore Foundation", "grant_number": "GBMF-4306" }, { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/jhep03(2021)094", "primary_object": { "basename": "2012.01620.pdf", "url": "https://authors.library.caltech.edu/records/9fh52-1es68/files/2012.01620.pdf" }, "related_objects": [ { "basename": "Zhang2021_Article_AnObstacleToSub-AdSHolographyF.pdf", "url": "https://authors.library.caltech.edu/records/9fh52-1es68/files/Zhang2021_Article_AnObstacleToSub-AdSHolographyF.pdf" } ], "resource_type": "article", "pub_year": "2021", "author_list": "Zhang, Pengfei; Gu, Yingfei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0d47f-80551", "eprint_id": 108541, "eprint_status": "archive", "datestamp": "2023-08-20 02:04:47", "lastmod": "2023-10-20 23:02:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dadras-Pouria", "name": { "family": "Dadras", "given": "Pouria" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" } ] }, "title": "Perturbative calculations of entanglement entropy", "ispublished": "pub", "full_text_status": "public", "keywords": "AdS-CFT Correspondence, Black Holes, 2D Gravity", "note": "\u00a9 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.\nArticle funded by SCOAP3.\n\nReceived: December 11, 2020;\nAccepted: February 5, 2021;\nPublished: March 22, 2021.\n\nWe thank Douglas Stanford, Juan Maldacena, Pengfei Zhang, and Yiming Chen for useful\ndiscussions. We gratefully acknowledge the support by the Simons Foundation under\ngrant 376205. A.K. is also supported by the Simons Foundation through the \"It from\nQubit\" program, as well as by the Institute of Quantum Information and Matter, a NSF\nFrontier center funded in part by the Gordon and Betty Moore Foundation.\n\nPublished - Dadras-Kitaev2021_Article_PerturbativeCalculationsOfEnta.pdf
Submitted - 2011.09622.pdf
", "abstract": "This paper is an attempt to extend the recent understanding of the Page curve for evaporating black holes to more general systems coupled to a heat bath. Although calculating the von Neumann entropy by the replica trick is usually a challenge, we have identified two solvable cases. For the initial section of the Page curve, we sum up the perturbation series in the system-bath coupling \u03ba; the most interesting contribution is of order 2s, where s is the number of replicas. For the saturated regime, we consider the effect of an external impulse on the entropy at a later time and relate it to OTOCs. A significant simplification occurs in the maximal chaos case such that the effect may be interpreted in terms of an intermediate object, analogous to the branching surface of a replica wormhole.", "date": "2021-03", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2021", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 198", "id_number": "CaltechAUTHORS:20210324-090318969", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210324-090318969", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "IQIM" } ] }, "doi": "10.1007/jhep03(2021)198", "primary_object": { "basename": "2011.09622.pdf", "url": "https://authors.library.caltech.edu/records/0d47f-80551/files/2011.09622.pdf" }, "related_objects": [ { "basename": "Dadras-Kitaev2021_Article_PerturbativeCalculationsOfEnta.pdf", "url": "https://authors.library.caltech.edu/records/0d47f-80551/files/Dadras-Kitaev2021_Article_PerturbativeCalculationsOfEnta.pdf" } ], "resource_type": "article", "pub_year": "2021", "author_list": "Dadras, Pouria and Kitaev, Alexei" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ws4nr-5nm95", "eprint_id": 106429, "eprint_status": "archive", "datestamp": "2023-08-20 00:18:17", "lastmod": "2023-10-20 23:28:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lunkin-A-V", "name": { "family": "Lunkin", "given": "A.\u2009V." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A.\u2009Yu." }, "orcid": "0000-0002-5777-642X" }, { "id": "Feigel'man-M-V", "name": { "family": "Feigel'man", "given": "M.\u2009V." }, "orcid": "0000-0002-7114-5296" } ] }, "title": "Perturbed Sachdev-Ye-Kitaev Model: A Polaron in the Hyperbolic Plane", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 American Physical Society. \n\nReceived 5 July 2020; accepted 2 October 2020; published 3 November 2020. \n\nM.\u2009V.\u2009F. is grateful to L.\u2009B. Ioffe, A. Kamenev, V.\u2009E. Kravtsov, and K.\u2009S. Tikhonov for useful discussions. Research of A.\u2009V.\u2009L. was partially supported by the Foundation for Advancement of Theoretical Physics and Mathematics \"Basis\" and Basic research program of HSE.\u2009A.\u2009K. is supported by the Simons Foundation under Grant No. 376205 and through the \"It from Qubit\" program, as well as by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation.\n\nPublished - PhysRevLett.125.196602.pdf
Submitted - 2006.14535.pdf
Supplemental Material - SM.pdf
", "abstract": "We study the Sachdev-Ye-Kitaev (SYK\u2084) model with a weak SYK\u2082 term of magnitude \u0393 beyond the simplest perturbative limit considered previously. For intermediate values of the perturbation strength, J/N \u226a \u0393 \u226a J/\u221aN, fluctuations of the Schwarzian mode are suppressed, and the SYK\u2084 mean-field solution remains valid beyond the timescale t\u2080 \u223c N/J up to t\u2217\u223cJ/\u0393\u00b2. The out-of-time-order correlation function displays at short time intervals exponential growth with maximal Lyapunov exponent 2\u03c0T, but its prefactor scales as T at low temperatures T \u2264 \u0393.", "date": "2020-11-06", "date_type": "published", "publication": "Physical Review Letters", "volume": "125", "number": "19", "publisher": "American Physical Society", "pagerange": "Art. No. 196602", "id_number": "CaltechAUTHORS:20201104-130324443", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201104-130324443", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Foundation for Advancement of Theoretical Physics" }, { "agency": "National Research University (Russia)" }, { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute of Quantum Information and Matter (IQIM)" }, { "agency": "Gordon and Betty Moore Foundation" } ] }, "local_group": { "items": [ { "id": "IQIM" } ] }, "doi": "10.1103/physrevlett.125.196602", "primary_object": { "basename": "SM.pdf", "url": "https://authors.library.caltech.edu/records/ws4nr-5nm95/files/SM.pdf" }, "related_objects": [ { "basename": "2006.14535.pdf", "url": "https://authors.library.caltech.edu/records/ws4nr-5nm95/files/2006.14535.pdf" }, { "basename": "PhysRevLett.125.196602.pdf", "url": "https://authors.library.caltech.edu/records/ws4nr-5nm95/files/PhysRevLett.125.196602.pdf" } ], "resource_type": "article", "pub_year": "2020", "author_list": "Lunkin, A.\u2009V.; Kitaev, A.\u2009Yu.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yjd75-2ph48", "eprint_id": 101578, "eprint_status": "archive", "datestamp": "2023-08-22 03:51:57", "lastmod": "2023-10-19 22:52:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gu-Yingfei", "name": { "family": "Gu", "given": "Yingfei" }, "orcid": "0000-0001-8645-879X" }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Sachdev-S", "name": { "family": "Sachdev", "given": "Subir" }, "orcid": "0000-0002-2432-7070" }, { "id": "Tarnopolsky-G", "name": { "family": "Tarnopolsky", "given": "Grigory" } } ] }, "title": "Notes on the complex Sachdev-Ye-Kitaev model", "ispublished": "pub", "full_text_status": "public", "keywords": "Holography and condensed matter physics (AdS/CMT); AdS-CFT Correspondence; Models of Quantum Gravity", "note": "\u00a9 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: November 13, 2019; Accepted: February 4, 2020; Published: February 25, 2020. \n\nWe thank Wenbo Fu, Antoine Georges, Simone Giombi, Luca Iliesiu, Igor Klebanov, Sung-Sik Lee, Juan Maldacena, Olivier Parcollet, Xiao-Liang Qi, Shinsei Ryu, Wei Song, Douglas Stanford and Cenke Xu for useful discussions. Y.G. is supported by the Gordon and Betty\nMoore Foundation EPiQS Initiative through Grant (GBMF-4306) and DOE grant, DE-SC0019030. A.K. is supported by the Simons Foundation under grant 376205 and through the \"It from Qubit\" program, as well as by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation. S.S. and G.T. are supported by DOE grant, DE-SC0019030. G.T. acknowledges support from the MURI grant W911NF-14-1-0003 from ARO and by DOE grant DE-SC0007870. This work was performed in part at KITP, University of California, Santa Barbara supported by the NSF under grant PHY-1748958.\n\nPublished - Gu2020_Article_NotesOnTheComplexSachdev-Ye-Ki.pdf
Submitted - 1910.14099.pdf
", "abstract": "We describe numerous properties of the Sachdev-Ye-Kitaev model for complex fermions with N\u2009\u226b\u20091 flavors and a global U(1) charge. We provide a general definition of the charge in the (G, \u03a3) formalism, and compute its universal relation to the infrared asymmetry of the Green function. The same relation is obtained by a renormalization theory. The conserved charge contributes a compact scalar field to the effective action, from which we derive the many-body density of states and extract the charge compressibility. We compute the latter via three distinct numerical methods and obtain consistent results. Finally, we present a two dimensional bulk picture with free Dirac fermions for the zero temperature entropy.", "date": "2020-02", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2020", "number": "2", "publisher": "Springer", "pagerange": "Art. No. 157", "id_number": "CaltechAUTHORS:20200226-133542550", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200226-133542550", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Gordon and Betty Moore Foundation", "grant_number": "GBMF-4306" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0019030" }, { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute of Quantum Information and Matter (IQIM)" }, { "agency": "Army Research Office (ARO)", "grant_number": "W911NF-14-1-0003" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0007870" }, { "agency": "NSF", "grant_number": "PHY-1748958" } ] }, "local_group": { "items": [ { "id": "IQIM" } ] }, "doi": "10.1007/jhep02(2020)157", "primary_object": { "basename": "1910.14099.pdf", "url": "https://authors.library.caltech.edu/records/yjd75-2ph48/files/1910.14099.pdf" }, "related_objects": [ { "basename": "Gu2020_Article_NotesOnTheComplexSachdev-Ye-Ki.pdf", "url": "https://authors.library.caltech.edu/records/yjd75-2ph48/files/Gu2020_Article_NotesOnTheComplexSachdev-Ye-Ki.pdf" } ], "resource_type": "article", "pub_year": "2020", "author_list": "Gu, Yingfei; Kitaev, Alexei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/apz8k-z2d79", "eprint_id": 95895, "eprint_status": "archive", "datestamp": "2023-08-22 01:30:59", "lastmod": "2023-10-20 20:41:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Suh-S-Josephine", "name": { "family": "Suh", "given": "S. Josephine" }, "orcid": "0000-0003-2393-6883" } ] }, "title": "Statistical mechanics of a two-dimensional black hole", "ispublished": "pub", "full_text_status": "public", "keywords": "2D Gravity; Black Holes; Models of Quantum Gravity; AdS-CFT Correspondence", "note": "\u00a9 2019 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: March 5, 2019; Accepted: May 20, 2019; Published: May 29, 2019.\n\nWe thank Daniel Jafferis, Juan Maldacena, Douglas Stanford, Herman Verlinde, and Zhenbin Yang for discussions. We gratefully acknowledge the support by the Simons Foundation through the \"It from Qubit\" program. A.K. is supported by the Simons Foundation under grant 376205 and by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.\n\nPublished - Kitaev-Suh2019_Article_StatisticalMechanicsOfATwo-dim.pdf
Submitted - 1808.07032.pdf
", "abstract": "The dynamics of a nearly-AdS_2 spacetime with boundaries is reduced to that of two particles in the anti-de Sitter space. We determine the class of physically meaningful wavefunctions, and prescribe the statistical mechanics of a black hole. We demonstrate how wavefunctions for a two-sided black hole and a regularized notion of trace can be used to construct thermal partition functions, and more generally, arbitrary density matrices. We also obtain correlation functions of external operators.", "date": "2019-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2019", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 198", "id_number": "CaltechAUTHORS:20190529-161258314", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190529-161258314", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "NSF", "grant_number": "PHY-1607611" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "IQIM" } ] }, "doi": "10.1007/JHEP05(2019)198", "primary_object": { "basename": "1808.07032.pdf", "url": "https://authors.library.caltech.edu/records/apz8k-z2d79/files/1808.07032.pdf" }, "related_objects": [ { "basename": "Kitaev-Suh2019_Article_StatisticalMechanicsOfATwo-dim.pdf", "url": "https://authors.library.caltech.edu/records/apz8k-z2d79/files/Kitaev-Suh2019_Article_StatisticalMechanicsOfATwo-dim.pdf" } ], "resource_type": "article", "pub_year": "2019", "author_list": "Kitaev, Alexei and Suh, S. Josephine" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/a8dc3-z4r02", "eprint_id": 92991, "eprint_status": "archive", "datestamp": "2023-08-22 00:49:26", "lastmod": "2023-10-20 16:42:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gu-Yingfei", "name": { "family": "Gu", "given": "Yingfei" }, "orcid": "0000-0001-8645-879X" }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } } ] }, "title": "On the relation between the magnitude and exponent of OTOCs", "ispublished": "pub", "full_text_status": "public", "keywords": "AdS-CFT Correspondence; 1/N Expansion; Models of Quantum Gravity", "note": "\u00a9 2019 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: January 15, 2019; Accepted: February 8, 2019; Published: February 13, 2019. \n\nWe thank David Huse, Juan Maldacena, Xiao-Liang Qi, Subir Sachdev, Steve Shenker, Douglas Stanford, Josephine Suh and Ashvin Vishwanath for useful discussions. Y.G. is supported by the Gordon and Betty Moore Foundation EPiQS Initiative through Grant (GBMF-4306). A.K. is supported by the Simons Foundation under grant 376205 and through the \"It from Qubit\" program, as well as by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611, and at KITP, supported by the NSF grant PHY-1748958.\n\nPublished - Gu-Kitaev2019_Article_OnTheRelationBetweenTheMagnitu.pdf
Submitted - 1812.00120.pdf
", "abstract": "We derive an identity relating the growth exponent of early-time OTOCs, the pre-exponential factor, and a third number called \"branching time\". The latter is defined within the dynamical mean-field framework, namely, in terms of the retarded kernel. This identity can be used to calculate stringy effects in the SYK and similar models; we also explicitly define \"strings\" in this context. As another application, we consider an SYK chain. If the coupling strength \u03b2J is above a certain threshold and nonlinear (in the magnitude of OTOCs) effects are ignored, the exponent in the butterfly wavefront is exactly 2\u03c0/\u03b2.", "date": "2019-02", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2019", "number": "2", "publisher": "Springer", "pagerange": "Art. No. 75", "id_number": "CaltechAUTHORS:20190220-075207560", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190220-075207560", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Gordon and Betty Moore Foundation", "grant_number": "GBMF-4306" }, { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "It from Qubit Program" }, { "agency": "Institute of Quantum Information and Matter (IQIM)" }, { "agency": "NSF", "grant_number": "PHY-1607611" }, { "agency": "NSF", "grant_number": "PHY-1748958" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "IQIM" } ] }, "doi": "10.1007/JHEP02(2019)075", "primary_object": { "basename": "1812.00120.pdf", "url": "https://authors.library.caltech.edu/records/a8dc3-z4r02/files/1812.00120.pdf" }, "related_objects": [ { "basename": "Gu-Kitaev2019_Article_OnTheRelationBetweenTheMagnitu.pdf", "url": "https://authors.library.caltech.edu/records/a8dc3-z4r02/files/Gu-Kitaev2019_Article_OnTheRelationBetweenTheMagnitu.pdf" } ], "resource_type": "article", "pub_year": "2019", "author_list": "Gu, Yingfei and Kitaev, Alexei" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pz4qv-6pf59", "eprint_id": 87568, "eprint_status": "archive", "datestamp": "2023-08-19 10:13:22", "lastmod": "2023-10-18 21:16:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Poulin-D", "name": { "family": "Poulin", "given": "David" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Steiger-D-S", "name": { "family": "Steiger", "given": "Damian S." } }, { "id": "Hastings-M-B", "name": { "family": "Hastings", "given": "Matthew B." } }, { "id": "Troyer-M", "name": { "family": "Troyer", "given": "Matthias" } } ] }, "title": "Quantum Algorithm for Spectral Measurement with a Lower Gate Count", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 American Physical Society. \n\n(Received 22 December 2017; published 5 July 2018) \n\nWe thank Thomas H\u00e4ner for interesting discussions and Sergey Bravyi for feedback, and acknowledge support by the Swiss National Science Foundation, the NCCR QSIT, Canada's NSERC, Caltech's IQIM, and the Simons Foundation.\n\nPublished - PhysRevLett.121.010501.pdf
", "abstract": "We present two techniques that can greatly reduce the number of gates required to realize an energy measurement, with application to ground state preparation in quantum simulations. The first technique realizes that to prepare the ground state of some Hamiltonian, it is not necessary to implement the time-evolution operator: any unitary operator which is a function of the Hamiltonian will do. We propose one such unitary operator which can be implemented exactly, circumventing any Taylor or Trotter approximation errors. The second technique is tailored to lattice models, and is targeted at reducing the use of generic single-qubit rotations, which are very expensive to produce by standard fault tolerant techniques. In particular, the number of generic single-qubit rotations used by our method scales with the number of parameters in the Hamiltonian, which contrasts with a growth proportional to the lattice size required by other techniques.", "date": "2018-07-06", "date_type": "published", "publication": "Physical Review Letters", "volume": "121", "number": "1", "publisher": "American Physical Society", "pagerange": "Art. No. 010501", "id_number": "CaltechAUTHORS:20180705-150616687", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180705-150616687", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Swiss National Science Foundation (SNSF)" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "IQIM" } ] }, "doi": "10.1103/PhysRevLett.121.010501", "primary_object": { "basename": "PhysRevLett.121.010501.pdf", "url": "https://authors.library.caltech.edu/records/pz4qv-6pf59/files/PhysRevLett.121.010501.pdf" }, "resource_type": "article", "pub_year": "2018", "author_list": "Poulin, David; Kitaev, Alexei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/68vgr-vj392", "eprint_id": 86710, "eprint_status": "archive", "datestamp": "2023-08-21 23:17:49", "lastmod": "2023-10-18 19:55:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Suh-S-Josephine", "name": { "family": "Suh", "given": "S. Josephine" }, "orcid": "0000-0003-2393-6883" } ] }, "title": "The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual", "ispublished": "pub", "full_text_status": "public", "keywords": "2D Gravity; AdS-CFT Correspondence; Black Holes; Models of Quantum Gravity", "note": "\u00a9 The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: April 2, 2018; Accepted: May 22, 2018; Published: May 29, 2018. \n\nWe thank Juan Maldacena, Douglas Stanford, and Yingfei Gu for useful discussions. We gratefully acknowledge the support by the Simons Foundation through the \"It from Qubit\" program. A.K. is supported by the Simons Foundation under grant 376205 and by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation. The work of J.S. was supported in part by the Natural Sciences and Engineering Research Council of Canada and by the Simons Foundation through grant 376206. It was performed in part at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.\n\nPublished - 10.1007_2FJHEP05_2018_183.pdf
Submitted - 1711.08467.pdf
", "abstract": "We give an exposition of the SYK model with several new results. A non-local correction to the Schwarzian effective action is found. The same action is obtained by integrating out the bulk degrees of freedom in a certain variant of dilaton gravity. We also discuss general properties of out-of-time-order correlators.", "date": "2018-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2018", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 183", "id_number": "CaltechAUTHORS:20180530-110303978", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180530-110303978", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Simons Foundation", "grant_number": "376206" }, { "agency": "NSF", "grant_number": "PHY-1607611" } ] }, "local_group": { "items": [ { "id": "IQIM" } ] }, "doi": "10.1007/JHEP05(2018)183", "primary_object": { "basename": "10.1007_2FJHEP05_2018_183.pdf", "url": "https://authors.library.caltech.edu/records/68vgr-vj392/files/10.1007_2FJHEP05_2018_183.pdf" }, "related_objects": [ { "basename": "1711.08467.pdf", "url": "https://authors.library.caltech.edu/records/68vgr-vj392/files/1711.08467.pdf" } ], "resource_type": "article", "pub_year": "2018", "author_list": "Kitaev, Alexei and Suh, S. Josephine" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zr4ma-33g67", "eprint_id": 68639, "eprint_status": "archive", "datestamp": "2023-08-20 12:23:38", "lastmod": "2023-10-19 22:24:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Burnell-F-J", "name": { "family": "Burnell", "given": "Fiona" } }, { "id": "Chen-Xie", "name": { "family": "Chen", "given": "Xie" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Metlitski-M-A", "name": { "family": "Metlitski", "given": "Max" } }, { "id": "Vishwanath-A", "name": { "family": "Vishwanath", "given": "Ashvin" } } ] }, "title": "Time reversal invariant gapped boundaries of the double semion state", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 American Physical Society. \n\nReceived 30 March 2016; published 30 June 2016. \n\nWe would like to thank Lukasz Fidkowski, Zhenghan Wang, Meng Cheng, and T. Senthil for discussion. X.C. is supported by the Miller Institute for Basic Research in Science at UC Berkeley, the Caltech Institute for Quantum Information and Matter and the Walter Burke Institute for Theoretical Physics. A.V. is supported by the Templeton Foundation. FJB is supported by NSF DMR-1352271 and Sloan FG-2015-65927.\n\nPublished - PhysRevB.93.235161.pdf
Submitted - 1509.00355v1.pdf
", "abstract": "The boundary of a fractionalized topological phase can be gapped by condensing a proper set of bosonic quasiparticles. Interestingly, in the presence of a global symmetry, such a boundary can have different symmetry transformation properties. Here we present an explicit example of this kind, in the double semion state with time reversal symmetry. We find two distinct cases where the semionic excitations on the boundary can transform either as time reversal singlets or as time reversal (Kramers) doublets, depending on the coherent phase factor of the Bose condensate. The existence of these two possibilities are demonstrated using both field-theory argument and exactly solvable lattice models. Furthermore, we study the domain walls between these two types of gapped boundaries and find that the application of time reversal symmetry tunnels a semion between them.", "date": "2016-06-15", "date_type": "published", "publication": "Physical Review B", "volume": "93", "number": "23", "publisher": "American Physical Society", "pagerange": "Art. No. 235161", "id_number": "CaltechAUTHORS:20160623-125613186", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160623-125613186", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Miller Institute for Basic Research in Science" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Templeton Foundation" }, { "agency": "NSF", "grant_number": "DMR-1352271" }, { "agency": "Alfred P. Sloan Foundation", "grant_number": "FG-2015-65927" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1103/PhysRevB.93.235161", "primary_object": { "basename": "1509.00355v1.pdf", "url": "https://authors.library.caltech.edu/records/zr4ma-33g67/files/1509.00355v1.pdf" }, "related_objects": [ { "basename": "PhysRevB.93.235161.pdf", "url": "https://authors.library.caltech.edu/records/zr4ma-33g67/files/PhysRevB.93.235161.pdf" } ], "resource_type": "article", "pub_year": "2016", "author_list": "Burnell, Fiona; Chen, Xie; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hgwzf-ttf17", "eprint_id": 70983, "eprint_status": "archive", "datestamp": "2023-08-20 00:50:18", "lastmod": "2023-10-23 15:14:32", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Eisentr\u00e4ger-K", "name": { "family": "Eisentr\u00e4ger", "given": "Kirsten" } }, { "id": "Hallgren-S", "name": { "family": "Hallgren", "given": "Sean" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Song-Fang", "name": { "family": "Song", "given": "Fang" } } ] }, "title": "A quantum algorithm for computing the unit group of an arbitrary degree number field", "ispublished": "unpub", "full_text_status": "public", "keywords": "Algorithms, Theory, Quantum Algorithms, Unit Group, Computational Algebraic Number Theory", "note": "Copyright is held by the owner/author(s). \n\nPartially supported by National Science Foundation grant DMS-1056703 and by the National Security Agency (NSA) under Army Research Office (ARO) contract number W911NF-12-1-0522. Part of this work was done while the first author was visiting Harvard University and MIT. \n\nPartially supported by National Science Foundation awards CCF-0747274 and CCF-1218721, and by the National Security Agency (NSA) under Army Research Office (ARO) contract number W911NF-12-1-0522. Part of this work was done while visiting MIT.\n\nPublished - p293-eisentrager.pdf
", "abstract": "Computing the group of units in a field of algebraic numbers\nis one of the central tasks of computational algebraic number theory. It is believed to be hard classically, which is of interest for cryptography. In the quantum setting, efficient algorithms were previously known for fields of constant degree. We give a quantum algorithm that is polynomial in the degree of the field and the logarithm of its discriminant. This is achieved by combining three new results. The first is a classical algorithm for computing a basis for certain ideal lattices with doubly exponentially large generators. The second shows that a Gaussian-weighted superposition of lattice points, with an appropriate encoding, can be used to provide a unique representation of a real-valued lattice. The third is an extension of the hidden subgroup problem to continuous groups and a quantum algorithm for solving the HSP over the group \u211d^n.", "date": "2014-05", "date_type": "published", "publisher": "ACM", "place_of_pub": "New York, NY", "pagerange": "293-302", "id_number": "CaltechAUTHORS:20161010-172823440", "isbn": "978-1-4503-2710-7", "book_title": "STOC '14 Proceedings of the 46th Annual ACM Symposium on Theory of Computing", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161010-172823440", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1056703" }, { "agency": "Army Research Office (ARO)", "grant_number": "W911NF-12-1-0522" }, { "agency": "NSF", "grant_number": "CCF-0747274" }, { "agency": "NSF", "grant_number": "CCF-1218721" }, { "agency": "National Security Agency" } ] }, "contributors": { "items": [ { "id": "Shmoys-D", "name": { "family": "Shmoys", "given": "David" } } ] }, "doi": "10.1145/2591796.2591860", "primary_object": { "basename": "p293-eisentrager.pdf", "url": "https://authors.library.caltech.edu/records/hgwzf-ttf17/files/p293-eisentrager.pdf" }, "resource_type": "book_section", "pub_year": "2014", "author_list": "Eisentr\u00e4ger, Kirsten; Hallgren, Sean; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/f9txd-6jq82", "eprint_id": 43591, "eprint_status": "archive", "datestamp": "2023-08-19 14:18:46", "lastmod": "2023-10-25 23:41:32", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Arad-Itai", "name": { "family": "Arad", "given": "Itai" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Landau-Zeph", "name": { "family": "Landau", "given": "Zeph" } }, { "id": "Vazirani-Umesh-V", "name": { "family": "Vazirani", "given": "Umesh" } } ] }, "title": "An area law and sub-exponential algorithm for 1D systems", "ispublished": "unpub", "full_text_status": "public", "note": "We are grateful to Dorit Aharonov, Fernando Brandao, and Matt Hastings for inspiring discussions\nabout the above and related topics.\n\nSubmitted - 1301.1162v1.pdf
", "abstract": "We give a new proof for the area law for general 1D gapped systems, which exponentially improves Hastings' famous result [1]. Specifically, we show that for a chain of d-dimensional spins, governed by a 1D local Hamiltonian with a spectral gap \u03b5 > 0, the entanglement entropy of the ground state with respect to any cut in the chain is upper bounded by O(log^3 d/\u03b5 ). Our approach uses the framework of Refs. [2, 3] to construct a Chebyshev-based AGSP (Approximate Ground Space Projection) with favorable factors. However, our construction uses the Hamiltonian directly, instead of using the Detectability lemma, which allows us to work with general (frustrated) Hamiltonians, as well as slightly improving the 1/\u03b5 dependence of the bound in Ref. [3]. To achieve that, we establish a new, \"random-walk like\", bound on the entanglement rank of an arbitrary power of a 1D Hamiltonian, which might be of independent interest: ER(H^\u2113) \u2264 (\u2113d)O(\u221a\u2113). Finally, treating d as a constant, our AGSP shows that the ground state is well approximated by a matrix product state with a sublinear bond dimension B = \u03b5 ^O(log^(3/4) n/\u03b5^(1/4)). Using this in conjunction with known dynamical programing algorithms, yields an algorithm for a 1=poly(n) approximation of the ground energy with a subexponential running time T \u2264 exp (\u03b5O(log^(3/4) n/\u03b5^(1/4))).", "date": "2014-01-30", "date_type": "published", "id_number": "CaltechAUTHORS:20140130-142058060", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140130-142058060", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "IQIM" } ] }, "doi": "10.48550/arXiv.1301.1162v1", "primary_object": { "basename": "1301.1162v1.pdf", "url": "https://authors.library.caltech.edu/records/f9txd-6jq82/files/1301.1162v1.pdf" }, "resource_type": "monograph", "pub_year": "2014", "author_list": "Arad, Itai; Kitaev, Alexei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/v84kc-nd242", "eprint_id": 38982, "eprint_status": "archive", "datestamp": "2023-08-19 19:53:19", "lastmod": "2023-10-24 14:55:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Brooks-P", "name": { "family": "Brooks", "given": "Peter" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" } } ] }, "title": "Protected gates for superconducting qubits", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 American Physical Society\nReceived 21 February 2013; published 6 May 2013.\nWe thank David DiVincenzo for helpful discussions. This\nwork was supported in part by the Intelligence Advanced\nResearch Projects Activity (IARPA) via Department of Interior\nNational Business Center Contract No. D11PC20165. The US\ngovernment is authorized to reproduce and distribute reprints\nfor governmental purposes notwithstanding any copyright\nannotation thereon. The views and conclusions contained\nherein are those of the author and should not be interpreted\nas necessarily representing the official policies or\nendorsements, either expressed or implied, of Intelligence\nAdvanced Research Projects Activity, DoINBC, or the US\ngovernment. We also acknowledge support from National\nScience Foundation (NSF) Grant No. PHY-0803371, Department\nof Energy Grant No. DE-FG03-92-ER40701, and\nNational Security Agency/Army Research Office Grant No.\nW911NF-09-1-0442. The Institute for Quantum Information\nand Matter (IQIM) is an NSF Physics Frontiers Center with\nsupport from the Gordon and Betty Moore Foundation.\n\nPublished - PhysRevA.87.052306.pdf
Submitted - 1302.4122v1.pdf
", "abstract": "We analyze the accuracy of quantum phase gates acting on \"0-\u03c0 qubits\" in superconducting circuits, where the gates are protected against thermal and Hamiltonian noise by continuous-variable quantum error-correcting codes. The gates are executed by turning on and off a tunable Josephson coupling between an LC oscillator and a qubit or pair of qubits; assuming perfect qubits, we show that the gate errors are exponentially small when the oscillator's impedance \u221aL/C is large compared to \u210f/4e^2\u22481 k\u03a9. The protected gates are not computationally universal by themselves, but a scheme for universal fault-tolerant quantum computation can be constructed by combining them with unprotected noisy operations. We validate our analytic arguments with numerical simulations.", "date": "2013-05-06", "date_type": "published", "publication": "Physical Review A", "volume": "87", "number": "5", "publisher": "American Physical Society", "pagerange": "Art. No. 052306", "id_number": "CaltechAUTHORS:20130619-094717394", "issn": "1050-2947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130619-094717394", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Intelligence Advanced Research Projects Activity (IARPA)" }, { "agency": "Department of Interior National Business Center", "grant_number": "D11PC20165" }, { "agency": "NSF", "grant_number": "PHY-0803371" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "National Security Agency (NSA)/Army Research Office (ARO)", "grant_number": "W911NF-09-1-0442" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "NSF Physics Frontiers Center" }, { "agency": "Gordon and Betty Moore Foundation" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Caltech-Theory" } ] }, "doi": "10.1103/PhysRevA.87.052306", "primary_object": { "basename": "1302.4122v1.pdf", "url": "https://authors.library.caltech.edu/records/v84kc-nd242/files/1302.4122v1.pdf" }, "related_objects": [ { "basename": "PhysRevA.87.052306.pdf", "url": "https://authors.library.caltech.edu/records/v84kc-nd242/files/PhysRevA.87.052306.pdf" } ], "resource_type": "article", "pub_year": "2013", "author_list": "Brooks, Peter; Kitaev, Alexei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ga32c-ryy04", "eprint_id": 32413, "eprint_status": "archive", "datestamp": "2023-08-19 13:05:11", "lastmod": "2023-10-17 23:48:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Faoro-L", "name": { "family": "Faoro", "given": "Lara" } }, { "id": "Ioffe-L-B", "name": { "family": "Ioffe", "given": "Lev" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } } ] }, "title": "Dissipationless dynamics of randomly coupled spins at high temperatures", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 American Physical Society. \n\nReceived 1 February 2012; published 15 October 2012. \n\nWe are grateful to R. McDermott for the discussion of the experimental situation. This work was supported, in part, by Triangle de la physique 2007-36, ANR-06-BLAN-0218, ECS-0608842, ARO W911-09-1-0395, DARPA HR0011-09-1-0009. A.K. acknowledges funding by the Institute of Quantum Information under NSF Grant No. PHY-0803371.\n\nPublished - PhysRevB.86.134414.pdf
Submitted - 1112.3855v1.pdf
", "abstract": "We develop a technique to compute the high-frequency asymptotics of spin correlators in weakly interacting disordered spin systems. We show that the dynamical spin correlator decreases exponentially at high frequencies \u27e8SS\u27e9_\u03c9 \u223c exp(\u2212\u03c4\u2217\u03c9) and compute the characteristic time \u03c4\u2217 of this dependence. In a typical random configuration, some fraction of spins form strongly coupled pairs, which behave as two-level systems. Their switching dynamics is driven by the high-frequency noise from the surrounding spins, resulting in low-frequency 1/f noise in the magnetic susceptibility and other physical quantities. We discuss application of these results to the problem of susceptibility and flux noise in superconducting circuits at mK temperatures.", "date": "2012-10-01", "date_type": "published", "publication": "Physical Review B", "volume": "86", "number": "13", "publisher": "American Physical Society", "pagerange": "Art. No. 134414", "id_number": "CaltechAUTHORS:20120713-092458311", "issn": "1098-0121", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120713-092458311", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Triangle de la physique", "grant_number": "2007-36" }, { "agency": "Agence Nationale pour la Recherche (ANR)", "grant_number": "ANR-06-BLAN-0218" }, { "agency": "NSF", "grant_number": "ECS-0608842" }, { "agency": "Army Research Office (ARO)", "grant_number": "W911-09-1-0395" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR0011-09-1-0009" }, { "agency": "NSF", "grant_number": "PHY-0803371" } ] }, "local_group": { "items": [ { "id": "IQIM" } ] }, "doi": "10.1103/PhysRevB.86.134414", "primary_object": { "basename": "1112.3855v1.pdf", "url": "https://authors.library.caltech.edu/records/ga32c-ryy04/files/1112.3855v1.pdf" }, "related_objects": [ { "basename": "PhysRevB.86.134414.pdf", "url": "https://authors.library.caltech.edu/records/ga32c-ryy04/files/PhysRevB.86.134414.pdf" } ], "resource_type": "article", "pub_year": "2012", "author_list": "Faoro, Lara; Ioffe, Lev; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4nt3p-d2p84", "eprint_id": 35130, "eprint_status": "archive", "datestamp": "2023-08-19 12:55:08", "lastmod": "2023-10-20 15:23:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bell-M-T", "name": { "family": "Bell", "given": "M. T." } }, { "id": "Sadovskyy-I-A", "name": { "family": "Sadovskyy", "given": "I. A." } }, { "id": "Ioffe-L-B", "name": { "family": "Ioffe", "given": "L. B." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A. Yu." } }, { "id": "Gershenson-M-E", "name": { "family": "Gershenson", "given": "M. E." } } ] }, "title": "Quantum Superinductor with Tunable Nonlinearity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 American Physical Society.\n\nReceived 6 July 2012; published 27 September 2012.\nWe would like to thank V. Manucharyan and A.\nZamolodchikov for helpful discussions. The work was\nsupported by DARPA (HR0011-09-1-0009), NSF (DMR\n1006265), and ARO (W911NF-09-1-0395).\n\nPublished - PhysRevLett.109.137003.pdf
Supplemental Material - README.TXT
Supplemental Material - Supplement_v9.41.pdf
", "abstract": "We report on the realization of a superinductor, a dissipationless element whose microwave impedance greatly exceeds the resistance quantum R_Q. The design of the superinductor, implemented as a ladder of nanoscale Josephson junctions, enables tuning of the inductance and its nonlinearity by a weak magnetic field. The Rabi decay time of the superinductor-based qubit exceeds 1\u2009\u2009\u03bcs. The high kinetic inductance and strong nonlinearity offer new types of functionality, including the development of qubits protected from both flux and charge noises, fault tolerant quantum computing, and high-impedance isolation for electrical current standards based on Bloch oscillations.", "date": "2012-09-27", "date_type": "published", "publication": "Physical Review Letters", "volume": "109", "number": "13", "publisher": "American Physical Society", "pagerange": "Art. No. 137003", "id_number": "CaltechAUTHORS:20121026-145953727", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20121026-145953727", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR0011-09-1-0009" }, { "agency": "NSF", "grant_number": "DMR 1006265" }, { "agency": "Army Research Office (ARO)", "grant_number": "W911NF-09-1-0395" } ] }, "doi": "10.1103/PhysRevLett.109.137003", "primary_object": { "basename": "PhysRevLett.109.137003.pdf", "url": "https://authors.library.caltech.edu/records/4nt3p-d2p84/files/PhysRevLett.109.137003.pdf" }, "related_objects": [ { "basename": "README.TXT", "url": "https://authors.library.caltech.edu/records/4nt3p-d2p84/files/README.TXT" }, { "basename": "Supplement_v9.41.pdf", "url": "https://authors.library.caltech.edu/records/4nt3p-d2p84/files/Supplement_v9.41.pdf" } ], "resource_type": "article", "pub_year": "2012", "author_list": "Bell, M. T.; Sadovskyy, I. A.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tf8r6-qs172", "eprint_id": 32421, "eprint_status": "archive", "datestamp": "2023-08-19 10:37:37", "lastmod": "2023-10-17 23:48:25", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Wang-Zhenghan", "name": { "family": "Wang", "given": "Zhenghan" }, "orcid": "0000-0002-5253-6400" } ] }, "title": "Solutions to generalized Yang-Baxter equations via ribbon fusion categories", "ispublished": "unpub", "full_text_status": "public", "note": "The second author is partially supported by NSF DMS 1108736 and would like to thank E.\nRowell for observing (3) of Thm. 2.5, S. Hong for helping on 6j symbols, and R. Chen for\nnumerically testing the solutions.\n\nSubmitted - 1203.1063v2.pdf
", "abstract": "Inspired by quantum information theory, we look for representations of the braid groups B_n on V^(\u2297(n+m\u22122)) for some fixed vector space V such\nthat each braid generator \u03c3_i, i = 1, ..., n\u22121, acts on m consecutive tensor factors\nfrom i through i +m\u22121. The braid relation for m = 2 is essentially the Yang-Baxter equation, and the cases for m > 2 are called generalized Yang-Baxter\nequations. We observe that certain objects in ribbon fusion categories naturally give rise to such representations for the case m = 3. Examples are given\nfrom the Ising theory (or the closely related SU(2)_2), SO(N)_2 for N odd, and\nSU(3)_3. The solution from the Jones-Kauffman theory at a 6th root of unity,\nwhich is closely related to SO(3)_2 or SU(2)_4, is explicitly described in the end.", "date": "2012-07-19", "date_type": "published", "id_number": "CaltechAUTHORS:20120713-102318475", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120713-102318475", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1108736" } ] }, "local_group": { "items": [ { "id": "IQIM" } ] }, "doi": "10.48550/arXiv.1203.1063", "primary_object": { "basename": "1203.1063v2.pdf", "url": "https://authors.library.caltech.edu/records/tf8r6-qs172/files/1203.1063v2.pdf" }, "resource_type": "monograph", "pub_year": "2012", "author_list": "Kitaev, Alexei and Wang, Zhenghan" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/f6k80-j2g14", "eprint_id": 32603, "eprint_status": "archive", "datestamp": "2023-08-19 11:31:18", "lastmod": "2023-10-18 14:35:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Kong-Liang", "name": { "family": "Kong", "given": "Liang" } } ] }, "title": "Models for Gapped Boundaries and Domain Walls", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 Springer-Verlag.\n\n24 May 2011; Accepted: 18 January 2012; Published online: 7 June 2012.\n\nLK thanks Robert K\u00f6nig for introducing the Levin-Wen model to him, and Xiao-Gang Wen for a valuable comment on the physical meaning of defects of codimension 3. We thank John Preskill, Hector Bombin, Anton Kapustin and Yong-ShiWu for many inspiring conversations. This work was supported\nin part by NSF under Grant No. PHY-0803371. AK is also supported by ARO under Grant No. W911NF-09-1-0442. LK is supported by the Gordon and Betty Moore Foundation through Caltech's Center for the Physics of Information, and NSF under Grant No. PHY-0803371, the Basic Research Young Scholars Program and the Initiative Scientific Research Program of Tsinghua University, and NSFC under Grant No. 11071134.\n\nSubmitted - 1104.5047.pdf
", "abstract": "We define a class of lattice models for two-dimensional topological phases with boundary such that both the bulk and the boundary excitations are gapped. The bulk\npart is constructed using a unitary tensor category C as in the Levin-Wen model, whereas the boundary is associated with amodule category over C.We also consider domainwalls\n(or defect lines) between different bulk phases.Adomainwall is transparent to bulk excitations if the corresponding unitary tensor categories are Morita equivalent. Defects of\nhigher codimension will also be studied. In summary, we give a dictionary between physical ingredients of lattice models and tensor-categorical notions.", "date": "2012-07", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "313", "number": "2", "publisher": "Springer", "pagerange": "351-373", "id_number": "CaltechAUTHORS:20120720-094651607", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120720-094651607", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0803371" }, { "agency": "Army Research Office (ARO)", "grant_number": "W911NF-09-1-0442" }, { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "Caltech Center for the Physics of Information" }, { "agency": "NSF", "grant_number": "PHY-0803371" }, { "agency": "Tsinghua University Basic Research Young Scholars Program" }, { "agency": "Tsinghua University Initiative Scientific Research Program" }, { "agency": "NSFC", "grant_number": "11071134" } ] }, "doi": "10.1007/s00220-012-1500-5", "primary_object": { "basename": "1104.5047.pdf", "url": "https://authors.library.caltech.edu/records/f6k80-j2g14/files/1104.5047.pdf" }, "resource_type": "article", "pub_year": "2012", "author_list": "Kitaev, Alexei and Kong, Liang" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wzfgq-ewr80", "eprint_id": 22711, "eprint_status": "archive", "datestamp": "2023-08-19 05:34:12", "lastmod": "2023-10-23 17:09:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fidkowski-L", "name": { "family": "Fidkowski", "given": "Lukasz" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } } ] }, "title": "Topological phases of fermions in one dimension", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 American Physical Society. Received 13 September 2010; published 8 February 2011. We would like to acknowledge useful discussions with\nJason Alicea, Matthew Hastings, Netanel Lindner, John\nPreskill, Gil Refael, Ari Turner, and Dan Freed. A.K. is\ngrateful to the Aspen Center for Physics for hospitality.\nThis work was supported in part by the Institute for Quantum\nInformation under National Science Foundation Grant\nNo. PHY-0803371.\n\nPublished - Fidkowski2011p12796Phys_Rev_B.pdf
", "abstract": "In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of one-dimensional systems. We focus on the time-reversal-invariant Majorana chain (BDI symmetry class).While the band classification yields an integer topological index k, it is known that phases characterized by values of k in the same equivalence class modulo 8 can be adiabatically transformed one to another by adding suitable interaction terms. Here we show that the eight equivalence classes are distinct and exhaustive, and provide a physical interpretation for the interacting invariant modulo 8. The different phases realize different Altland-Zirnbauer classes of the reduced density matrix for an entanglement bipartition into two half chains. We generalize these results to the classification of all one-dimensional gapped phases of fermionic systems with possible antiunitary symmetries, utilizing the algebraic framework of central extensions. We use matrix product state methods to prove our results.", "date": "2011-02-15", "date_type": "published", "publication": "Physical Review B", "volume": "83", "number": "7", "publisher": "American Physical Society", "pagerange": "Art. No. 075103", "id_number": "CaltechAUTHORS:20110308-123056073", "issn": "1098-0121", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110308-123056073", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Institute for Quantum Information", "grant_number": "PHY-0803371" } ] }, "doi": "10.1103/PhysRevB.83.075103", "primary_object": { "basename": "Fidkowski2011p12796Phys_Rev_B.pdf", "url": "https://authors.library.caltech.edu/records/wzfgq-ewr80/files/Fidkowski2011p12796Phys_Rev_B.pdf" }, "resource_type": "article", "pub_year": "2011", "author_list": "Fidkowski, Lukasz and Kitaev, Alexei" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pcj8r-qnk44", "eprint_id": 22949, "eprint_status": "archive", "datestamp": "2023-08-19 05:33:17", "lastmod": "2023-10-23 17:45:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Tikhonov-K-S", "name": { "family": "Tikhonov", "given": "K. S." } }, { "id": "Feigel'man-M-V", "name": { "family": "Feigel'man", "given": "M. V." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A. Yu." } } ] }, "title": "Power-Law Spin Correlations in a Perturbed Spin Model on a Honeycomb Lattice", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 American Physical Society. Received 12 September 2010; revised 3 January 2011; published 11 February 2011. We are grateful to L. B. Ioffe and A. S. Ioselevich for\nuseful discussions. This research was supported by the\nRFBR Grant No. 10-02-00554.\n\nPublished - Tikhonov2011p12931Phys_Rev_Lett.pdf
", "abstract": "We consider the spin- 12 model on the honeycomb lattice in the presence of a weak magnetic field\nh_\u03b1 \u226a 1. Such a perturbation destroys the exact integrability of the model in terms of gapless fermions and\nstatic Z_2 fluxes. We show that it results in the appearance of a long-range tail in the irreducible dynamic\nspin correlation function: \u226as^z(t,r)s^z(0,0)\u226b \u03b1 h^2_z\nf(tr), where f(t,r) \u03b1 [max(t,r]^(-4) is proportional to the\ndensity polarization function of fermions.", "date": "2011-02-11", "date_type": "published", "publication": "Physical Review Letters", "volume": "106", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 067203", "id_number": "CaltechAUTHORS:20110316-161521086", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110316-161521086", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research (RFBR)", "grant_number": "10-02-00554" } ] }, "doi": "10.1103/PhysRevLett.106.067203", "primary_object": { "basename": "Tikhonov2011p12931Phys_Rev_Lett.pdf", "url": "https://authors.library.caltech.edu/records/pcj8r-qnk44/files/Tikhonov2011p12931Phys_Rev_Lett.pdf" }, "resource_type": "article", "pub_year": "2011", "author_list": "Tikhonov, K. S.; Feigel'man, M. V.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yq8z6-97a54", "eprint_id": 19810, "eprint_status": "archive", "datestamp": "2023-08-19 03:33:40", "lastmod": "2023-10-20 21:55:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Tupitsyn-I-S", "name": { "family": "Tupitsyn", "given": "I. S." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A." } }, { "id": "Prokof'ev-N-V", "name": { "family": "Prokof'ev", "given": "N. V." } }, { "id": "Stamp-P-C-E", "name": { "family": "Stamp", "given": "P. C. E." } } ] }, "title": "Topological multicritical point in the phase diagram of the toric code model and three-dimensional lattice gauge Higgs model", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 The American Physical Society.\n\nReceived 14 June 2010; published 17 August 2010.\n\nWe thank E. Fradkin, B. Svistunov, S. Trebst, M. Troyer,\nI. Affleck, K. Shtengel, and S. Sachdev for discussions. We\nare also indebted to M. Berciu and J. Heyl whose research\nclusters were used to perform our MC simulations. N.P. acknowledges\nsupport from the National Science Foundation\nunder Grant No. PHY-0653183, a grant from the Army Research\nOffice with funding from the DARPA OLE program,\nand Aspen Center for physics.\n\nPublished - Tupitsyn2010p11258Phys_Rev_B.pdf
", "abstract": "We construct a mapping between the two-dimensional toric code model in external magnetic fields, h_z and h_x, and the three-dimensional classical Ising system with plaquette interactions, which is equivalent to the three-dimensional Z_2 gauge Higgs model with anisotropy between the imaginary time and spatial directions. The isotropic limit of the latter model was studied using Monte Carlo simulations on large (up to 60^3) lattices in order to determine the stability of the topological phase against generic magnetic field perturbations and to resolve fine details of the phase diagram. We find that the topological phase is bounded by second-order transition lines, which merge into a first-order line at what appears to be a multicritical point arising from the competition between the Higgs and confinement transitions in the Z_2 gauge system. An effective field theory for this type of multicritical point (if one actually exists) is not known. Our results have potential applications to frustrated magnets, quantum computation, lattice gauge models in particle physics, and critical phenomena.", "date": "2010-08-17", "date_type": "published", "publication": "Physical Review B", "volume": "82", "number": "8", "publisher": "American Physical Society", "pagerange": "Art. No. 085114", "id_number": "CaltechAUTHORS:20100907-152559860", "issn": "1098-0121", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100907-152559860", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0653183" }, { "agency": "Army Research Office" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)" }, { "agency": "Aspen Center for Physics" } ] }, "doi": "10.1103/PhysRevB.82.085114", "primary_object": { "basename": "Tupitsyn2010p11258Phys_Rev_B.pdf", "url": "https://authors.library.caltech.edu/records/yq8z6-97a54/files/Tupitsyn2010p11258Phys_Rev_B.pdf" }, "resource_type": "article", "pub_year": "2010", "author_list": "Tupitsyn, I. S.; Kitaev, A.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cnwgn-76b14", "eprint_id": 18459, "eprint_status": "archive", "datestamp": "2023-08-19 02:10:04", "lastmod": "2023-10-20 16:24:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fidkowski-L", "name": { "family": "Fidkowski", "given": "Lukasz" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } } ] }, "title": "Effects of interactions on the topological classification of free fermion systems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 The American Physical Society. Received 4 January 2010; published 7 April 2010. We would like to acknowledge useful discussions with\nJohn Preskill and Andreas Ludwig. This work was supported\nin part by the Institute for Quantum Information under National\nScience Foundation, Grant No. PHY-0803371. A.K. is\nalso supported by DARPA under Grant No. HR0011-09-\n0009.\n\nPublished - Fidkowski2010p10059Phys_Rev_B.pdf
", "abstract": "We describe in detail a counterexample to the topological classification of free fermion systems. We deal with a one-dimensional chain of Majorana fermions with an unusual T symmetry. The topological invariant for the free fermion classification lies in Z, but with the introduction of interactions the Z is broken to Z_8. We illustrate this in the microscopic model of the Majorana chain by constructing an explicit path between two distinct phases whose topological invariants are equal modulo 8, along which the system remains gapped. The path goes through a strongly interacting region. We also find the field-theory interpretation of this phenomenon. There is a second-order phase transition between the two phases in the free theory, which can be avoided by going through the strongly interacting region. We show that this transition is in the two-dimensional Ising universality class, where a first-order phase transition line, terminating at a second-order transition, can be avoided by going through the analog of a high-temperature paramagnetic phase. In fact, we construct the full phase diagram of the system as a function of the thermal operator (i.e., the mass term that tunes between the two phases in the free theory) and two quartic operators, obtaining a first-order Peierls transition region, a second-order transition region, and a region with no transition.", "date": "2010-04-01", "date_type": "published", "publication": "Physical Review B", "volume": "81", "number": "13", "publisher": "American Physical Society", "pagerange": "Art. No. 134509", "id_number": "CaltechAUTHORS:20100526-114410284", "issn": "1098-0121", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100526-114410284", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Institute for Quantum Information under NSF", "grant_number": "PHY-0803371" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR0011-09-0009" } ] }, "doi": "10.1103/PhysRevB.81.134509", "primary_object": { "basename": "Fidkowski2010p10059Phys_Rev_B.pdf", "url": "https://authors.library.caltech.edu/records/cnwgn-76b14/files/Fidkowski2010p10059Phys_Rev_B.pdf" }, "resource_type": "article", "pub_year": "2010", "author_list": "Fidkowski, Lukasz and Kitaev, Alexei" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ps58j-7ha97", "eprint_id": 16903, "eprint_status": "archive", "datestamp": "2023-08-19 00:27:33", "lastmod": "2023-10-19 22:38:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gils-C", "name": { "family": "Gils", "given": "Charlotte" } }, { "id": "Trebst-S", "name": { "family": "Trebst", "given": "Simon" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Ludwig-A-W-W", "name": { "family": "Ludwig", "given": "Andreas W. W." } }, { "id": "Troyer-M", "name": { "family": "Troyer", "given": "Matthias" } }, { "id": "Wang-Zhenghan", "name": { "family": "Wang", "given": "Zhenghan" }, "orcid": "0000-0002-5253-6400" } ] }, "title": "Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 Macmillan Publishers Limited. \n\nReceived 18 September 2008; accepted 13 August 2009; published online 20 September 2009. \n\nWe thank M. Freedman, X.-G. Wen and P. Fendley for stimulating discussions. Our numerical simulations were based on the ALPS libraries. A.W.W.L. was supported, in part, by NSF DMR-0706140. \n\nAuthor contributions: C.G., S.T. and M.T. contributed to the numerical work. C.G., A.K., A.W.W.L and Z.W. contributed to the analytical solution. All authors contributed to the development of the general picture presented in this manuscript.\n\nSupplemental Material - Gils2009p6501Nat_Phys_supp.pdf
", "abstract": "Indistinguishable particles in two dimensions can be characterized by anyonic quantum statistics, which is more general than that of bosons or fermions. Anyons emerge as quasiparticles in fractional quantum Hall states and in certain frustrated quantum magnets. Quantum liquids of anyons show degenerate ground states, where the degeneracy depends on the topology of the underlying surface. Here, we present a new type of continuous quantum phase transition in such anyonic quantum liquids, which is driven by quantum fluctuations of the topology. The critical state connecting two anyonic liquids on surfaces with different topologies is reminiscent of the notion of a 'quantum foam' with fluctuations on all length scales. This exotic quantum phase transition arises in a microscopic model of interacting anyons for which we present an exact solution in a linear geometry. We introduce an intuitive physical picture of this model that unifies string nets and loop gases, and provide a simple description of topological quantum phases and their phase transitions.", "date": "2009-11", "date_type": "published", "publication": "Nature Physics", "volume": "5", "number": "11", "publisher": "Nature Publishing Group", "pagerange": "834-839", "id_number": "CaltechAUTHORS:20091208-111910640", "issn": "1745-2473", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20091208-111910640", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMR-0706140" } ] }, "doi": "10.1038/NPHYS1396", "primary_object": { "basename": "Gils2009p6501Nat_Phys_supp.pdf", "url": "https://authors.library.caltech.edu/records/ps58j-7ha97/files/Gils2009p6501Nat_Phys_supp.pdf" }, "resource_type": "article", "pub_year": "2009", "author_list": "Gils, Charlotte; Trebst, Simon; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zytbp-15b77", "eprint_id": 18207, "eprint_status": "archive", "datestamp": "2023-08-20 01:42:50", "lastmod": "2024-01-12 23:39:24", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } } ] }, "title": "Periodic table for topological insulators and superconductors", "ispublished": "unpub", "full_text_status": "public", "keywords": "phase transitions, localised states, fermion systems, Dirac equation, matrix algebra, superconducting materials", "note": "\u00a9 2009 American Institute of Physics.\n\nIssue Date: 14 May 2009.\n\nI am grateful to Andreas Ludwig and Shinsey Ryu for\nteaching me about ^(3)He-5 and (p_x + ip_y)\u2191 + (_Px - iP_y)\u2193\nand helping to fit these phases into the periodic table. I\nalso thank John Preskill, Michael Freedman, John Roe,\nCharles Kane, and Grigori Volovik for stimulating discussions. This research is supported in part by NSF under\ngrant No. PHY-0456720.\n\nPublished - Kitaev2009p8192Advances_In_Theoretical_Physics.pdf
", "abstract": "Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of real Clifford algebras. The phases within a given class are further characterized by a topological invariant, an element of some Abelian group that can be 0, Z, or Z_2. The interface between two infinite phases with different topological numbers must carry some gapless mode. Topological properties of finite systems are described in terms of K-homology. This classification is robust with respect to disorder, provided electron states near the Fermi energy are absent or localized. In some cases (e.g., integer quantum Hall systems) the K-theoretic classification is stable to interactions, but a counterexample is also given.", "date": "2009-05-14", "date_type": "published", "publisher": "American Institute of Physics", "place_of_pub": "New York, NY", "pagerange": "22-30", "id_number": "CaltechAUTHORS:20100510-100944960", "isbn": "978-0-7354-0671-1", "book_title": "Advances In Theoretical Physics: Landau Memorial Conference Chernogolokova (Russia), 22\u201326 June 2008", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100510-100944960", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0456720" } ] }, "contributors": { "items": [ { "id": "Lebedev-V", "name": { "family": "Lebedev", "given": "Vladimir" } }, { "id": "Feigel'man-M", "name": { "family": "Feigel'man", "given": "Mikhail" } } ] }, "doi": "10.1063/1.3149495", "primary_object": { "basename": "Kitaev2009p8192Advances_In_Theoretical_Physics.pdf", "url": "https://authors.library.caltech.edu/records/zytbp-15b77/files/Kitaev2009p8192Advances_In_Theoretical_Physics.pdf" }, "resource_type": "book_section", "pub_year": "2009", "author_list": "Kitaev, Alexei" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/a4tft-69g20", "eprint_id": 12496, "eprint_status": "archive", "datestamp": "2023-08-22 13:51:43", "lastmod": "2023-10-17 17:01:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Faoro-Lara", "name": { "family": "Faoro", "given": "Lara" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Ioffe-Lev-B", "name": { "family": "Ioffe", "given": "Lev B." } } ] }, "title": "Quasiparticle Poisoning and Josephson Current Fluctuations Induced by Kondo Impurities", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2008 The American Physical Society. \n\nReceived 25 January 2008; published 10 December 2008. \n\nThis work was supported by the National Security Agency (NSA) under Army Research Office (ARO) Contract No. W911NF-06-1-0208 and NSF ECS 0608842.\n\nPublished - FAOprl08.pdf
", "abstract": "We introduce a toy model that allows us to study the physical properties of a spin impurity coupled to the electrons in the superconducting island. We show that, when the coupling of the spin is of the order of the superconducting gap Delta, two almost degenerate subgap states are formed. By computing the Berry phase that is associated with the superconducting phase rotations in this model, we prove that these subgap states are characterized by a different charge and demonstrate that the switching between these states has the same effect as quasiparticle poisoning (unpoisoning) of the island. We also show that an impurity coupled to both the island and the lead generates Josepshon current fluctuations.", "date": "2008-12-12", "date_type": "published", "publication": "Physical Review Letters", "volume": "101", "number": "24", "publisher": "American Physical Society", "pagerange": "Art. No. 247002", "id_number": "CaltechAUTHORS:FAOprl08", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:FAOprl08", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "National Security Agency" }, { "agency": "Army Research Office (ARO)", "grant_number": "W911NF-06-1-0208" }, { "agency": "NSF", "grant_number": "ECS-0608842" } ] }, "collection": "CaltechAUTHORS", "doi": "10.1103/PhysRevLett.101.247002", "primary_object": { "basename": "FAOprl08.pdf", "url": "https://authors.library.caltech.edu/records/a4tft-69g20/files/FAOprl08.pdf" }, "resource_type": "article", "pub_year": "2008", "author_list": "Faoro, Lara; Kitaev, Alexei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9a9bg-hfq33", "eprint_id": 22054, "eprint_status": "archive", "datestamp": "2023-08-19 23:00:17", "lastmod": "2024-01-13 00:09:30", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Laumann-C", "name": { "family": "Laumann", "given": "Christopher" } } ] }, "title": "Topological phases and quantum computation", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2010 Oxford University Press. \n\nNotes written by C. Laumann.\n\nSubmitted - 0904.2771.pdf
", "abstract": "The basic building block of quantum computation is the qubit, a system with two (nearly)\ndegenerate states that can be used to encode quantum information. Real systems typically\nhave a full spectrum of excitations that are considered illegal from the point of view of a\ncomputation, and lead to decoherence if they couple too strongly into the qubit states during\nsome process (see Fig. 4.1). The essential problem, then, is to preserve the quantum state of\nthe qubit as long as possible to allow time for computations to take place.", "date": "2008-07", "date_type": "published", "publisher": "Oxford University Press", "place_of_pub": "Oxford", "pagerange": "101-125", "id_number": "CaltechAUTHORS:20110207-134954371", "isbn": "0-19-957461-8", "book_title": "Exact methods in low-dimensional statistical physics and quantum computing", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110207-134954371", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "contributors": { "items": [ { "id": "Jacobsen-J", "name": { "family": "Jacobsen", "given": "Jesper" } } ] }, "doi": "10.48550/arXiv.0904.2771", "primary_object": { "basename": "0904.2771.pdf", "url": "https://authors.library.caltech.edu/records/9a9bg-hfq33/files/0904.2771.pdf" }, "resource_type": "book_section", "pub_year": "2008", "author_list": "Kitaev, Alexei and Laumann, Christopher" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3bkfa-pm216", "eprint_id": 8641, "eprint_status": "archive", "datestamp": "2023-08-22 09:45:21", "lastmod": "2023-10-16 21:36:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Feldman-D-E", "name": { "family": "Feldman", "given": "D. E." } }, { "id": "Gefen-Y", "name": { "family": "Gefen", "given": "Yuval" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Law-K-T", "name": { "family": "Law", "given": "K. T." } }, { "id": "Stern-A", "name": { "family": "Stern", "given": "Ady" }, "orcid": "0000-0002-9493-268X" } ] }, "title": "Shot noise in an anyonic Mach-Zehnder interferometer", "ispublished": "pub", "full_text_status": "public", "keywords": "electron spin polarisation; Mach-Zehnder interferometers; quantum Hall effect; quasiparticles; shot noise", "note": "\u00a92007 The American Physical Society \n\n(Received 6 July 2007; published 21 August 2007) \n\nWe acknowledge the support by ARO under Grants Nos. W911NF-04-1-0236 (A.K.) and W911NF-05-1-0294) (A.K.), by NSF under Grants Nos. PHY99-07949 (D.E.F.), PHY-0456720 (A.K.), and DMR-0544116 (D.E.F. and K.T.L.), by the U.S.-Israel BSF (Y.G. and A.S.), the Minerva Foundation (A.S.), and the ISF of the Israel Academy of Sciences (Y.G.). D.E.F. acknowledges the hospitality of Microsoft Station Q and KITP in Santa Barbara.", "abstract": "We show how shot noise in an electronic Mach-Zehnder interferometer in the fractional quantum Hall regime probes the charge and statistics of quantum Hall quasiparticles. The dependence of the noise on the magnetic flux through the interferometer allows for a simple way to distinguish Abelian from non-Abelian quasiparticle statistics. In the Abelian case, the Fano factor (in units of the electron charge) is always lower than unity. In the non-Abelian case, the maximal Fano factor as a function of the magnetic flux exceeds 1.", "date": "2007-08-15", "date_type": "published", "publication": "Physical Review B", "volume": "76", "number": "8", "publisher": "Physical Review B", "pagerange": "Art. No. 085333", "id_number": "CaltechAUTHORS:FELprb07", "issn": "1098-0121", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:FELprb07", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1103/PhysRevB.76.085333", "primary_object": { "basename": "FELprb07.pdf", "url": "https://authors.library.caltech.edu/records/3bkfa-pm216/files/FELprb07.pdf" }, "resource_type": "article", "pub_year": "2007", "author_list": "Feldman, D. E.; Gefen, Yuval; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/w1fyp-hjm29", "eprint_id": 8566, "eprint_status": "archive", "datestamp": "2023-08-22 08:54:26", "lastmod": "2023-10-16 21:33:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Feiguin-A", "name": { "family": "Feiguin", "given": "Adrian" } }, { "id": "Trebst-S", "name": { "family": "Trebst", "given": "Simon" } }, { "id": "Ludwig-A-W-W", "name": { "family": "Ludwig", "given": "Andreas W. W." } }, { "id": "Troyer-M", "name": { "family": "Troyer", "given": "Matthis" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Wang-Zhenghan", "name": { "family": "Wang", "given": "Zhenghan" }, "orcid": "0000-0002-5253-6400" }, { "id": "Freedman-M-H", "name": { "family": "Freedman", "given": "Michael H." } } ] }, "title": "Interacting Anyons in Topological Quantum Liquids: The Golden Chain", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 The American Physical Society \n\n(Received 19 December 2006; published 20 April 2007) \n\nWe thank E. Ardonne, N. Bonesteel, P. Fendley, C. Nayak, G. Refael, S. H. Simon, and J. Slingerland for discussions.\n\nPublished - FEIprl07.pdf
", "abstract": "We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial (\"identity\") channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of a chain of Fibonacci anyons show that the model is critical with a dynamical critical exponent z=1, and described by a two-dimensional (2D) conformal field theory with central charge c=(7/10). An exact mapping of the anyonic chain onto the 2D tricritical Ising model is given using the restricted-solid-on-solid representation of the Temperley-Lieb algebra. The gaplessness of the chain is shown to have topological origin.", "date": "2007-04-20", "date_type": "published", "publication": "Physical Review Letters", "volume": "98", "number": "16", "publisher": "American Physical Society", "pagerange": "Art. No. 160409", "id_number": "CaltechAUTHORS:FEIprl07", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:FEIprl07", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1103/PhysRevLett.98.160409", "primary_object": { "basename": "FEIprl07.pdf", "url": "https://authors.library.caltech.edu/records/w1fyp-hjm29/files/FEIprl07.pdf" }, "resource_type": "article", "pub_year": "2007", "author_list": "Feiguin, Adrian; Trebst, Simon; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7hjm9-2r617", "eprint_id": 6188, "eprint_status": "archive", "datestamp": "2023-08-22 07:11:29", "lastmod": "2023-10-16 20:10:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Feldman-D-E", "name": { "family": "Feldman", "given": "D. E." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } } ] }, "title": "Detecting Non-Abelian Statistics with an Electronic Mach-Zehnder Interferometer", "ispublished": "pub", "full_text_status": "public", "note": "\u00a92006 The American Physical Society \n\n(Received 21 July 2006; published 3 November 2006) \n\nWe thank K.T. Law for the help with figures. A.K. acknowledges support by ARO under Grants No. W911NF-04-1-0236 and No. W911NF-05-1-0294 and by NSF under Grant No. PHY-0456720. D.E.F. acknowledges support by NSF under Grant No. DMR-0544116.", "abstract": "Fractionally charged quasiparticles in the quantum Hall state with a filling factor nu=5/2 are expected to obey non-Abelian statistics. We demonstrate that their statistics can be probed by transport measurements in an electronic Mach-Zehnder interferometer. The tunneling current through the interferometer exhibits a characteristic dependence on the magnetic flux and a nonanalytic dependence on the tunneling amplitudes which can be controlled by gate voltages.", "date": "2006-11-03", "date_type": "published", "publication": "Physical Review Letters", "volume": "97", "number": "18", "publisher": "American Physical Society", "pagerange": "Art. No. 186803", "id_number": "CaltechAUTHORS:FELprl06", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:FELprl06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "primary_object": { "basename": "FELprl06.pdf", "url": "https://authors.library.caltech.edu/records/7hjm9-2r617/files/FELprl06.pdf" }, "resource_type": "article", "pub_year": "2006", "author_list": "Feldman, D. E. and Kitaev, Alexei" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bs5y2-6qt49", "eprint_id": 3504, "eprint_status": "archive", "datestamp": "2023-08-22 05:24:02", "lastmod": "2023-10-16 15:57:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" } } ] }, "title": "Topological Entanglement Entropy", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum entanglement; quantum field theory; ground states; entropy; many-body problems; fermion systems", "note": "\u00a92006 The American Physical Society \n\n(Received 13 October 2005; published 24 March 2006) \n\nWe thank Anton Kapustin for discussions. This work has been supported in part by: the Department of Energy under Grant No. DE-FG03-92-ER40701, the National Science Foundation under Grant No. PHY-0456720, the Army Research Office under Grants No. W911NF-04-1-0236 and No. W911NF-05-1-0294, and the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374.", "abstract": "We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator rho for the degrees of freedom in the interior. The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho)=alphaL-gamma+[centered ellipsis], where the ellipsis represents terms that vanish in the limit L-->[infinity]. We show that -gamma is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for gamma in terms of properties of the superselection sectors of the medium.", "date": "2006-03-24", "date_type": "published", "publication": "Physical Review Letters", "volume": "96", "number": "11", "publisher": "American Physical Society", "pagerange": "Art. No. 110404", "id_number": "CaltechAUTHORS:KITprl06", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KITprl06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1103/PhysRevLett.96.110404", "primary_object": { "basename": "KITprl06.pdf", "url": "https://authors.library.caltech.edu/records/bs5y2-6qt49/files/KITprl06.pdf" }, "resource_type": "article", "pub_year": "2006", "author_list": "Kitaev, Alexei and Preskill, John" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cw614-xfy70", "eprint_id": 3919, "eprint_status": "archive", "datestamp": "2023-08-22 05:19:53", "lastmod": "2023-10-16 16:13:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kempe-J", "name": { "family": "Kempe", "given": "Julia" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Regev-O", "name": { "family": "Regev", "given": "Oded" } } ] }, "title": "The Complexity of the Local Hamiltonian Problem", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum computation, local Hamiltonian problem, complete problems, adiabatic computation", "note": "\u00a9 2006 SIAM \n\nReceived by the editors July 20, 2004; accepted for publication (in revised form) June 23, 2005; published electronically March 3, 2006. A preliminary version of this paper appeared in Proceedings of the 24th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), 2004. \n\nThis author's [JK] work was supported by ACI S\u00e9curit\u00e9 Informatique, 2003-n24; projet \"R\u00e9seaux Quantiques,\" ACI-CR 2002-40 and EU 5th framework program RESQ IST-2001-37559; by DARPA and Air Force Laboratory, Air Force Materiel Command, USAF, under agreement F30602-01-2-0524; by DARPA and the Office of Naval Research under grant FDN-00014-01-1-0826; and during a visit supported in part by the National Science Foundation under grant EIA-0086038 through the Institute for Quantum Information at the California Institute of Technology. \n\nThis author's [AK] work was supported in part by the National Science Foundation under grant EIA-0086038. \n\nThis author's [OR] work was supported by an Alon Fellowship, the Binational Science Foundation, the Israel Science Foundation, and the Army Research Office grant DAAD19-03-1-0082 and partly supported by ACI S\u00e9curit\u00e9 Informatique, 2003-n24, projet \"R\u00e9seaux Quantiques.\" Part of this author's work was carried out during a visit at LRI, Universit\u00e9 de Paris-Sud, and he thanks his hosts for their hospitality. \n\nDiscussions with Sergey Bravyi and Frank Verstraete are gratefully acknowledged.\n\nPublished - KEMsiamjc06.pdf
Submitted - 0406180.pdf
", "abstract": "The k-LOCAL Hamiltonian problem is a natural complete problem for the complexity class QMA, the quantum analogue of NP. It is similar in spirit to MAX-k-SAT, which is NP-complete for k >= 2. It was known that the problem is QMA-complete for any k >= 3. On the other hand, 1-LOCAL Hamiltonian is in P and hence not believed to be QMA-complete. The complexity of the 2-LOCAL Hamiltonian problem has long been outstanding. Here we settle the question and show that it is QMA-complete. We provide two independent proofs; our first proof uses only elementary linear algebra. Our second proof uses a powerful technique for analyzing the sum of two Hamiltonians; this technique is based on perturbation theory and we believe that it might prove useful elsewhere. Using our techniques we also show that adiabatic computation with 2-local interactions on qubits is equivalent to standard quantum computation.", "date": "2006-03-03", "date_type": "published", "publication": "SIAM Journal on Computing", "volume": "35", "number": "5", "publisher": "SIAM", "pagerange": "1070-1097", "id_number": "CaltechAUTHORS:KEMsiamjc06", "issn": "0097-5397", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KEMsiamjc06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1137/S0097539704445226", "primary_object": { "basename": "0406180.pdf", "url": "https://authors.library.caltech.edu/records/cw614-xfy70/files/0406180.pdf" }, "related_objects": [ { "basename": "KEMsiamjc06.pdf", "url": "https://authors.library.caltech.edu/records/cw614-xfy70/files/KEMsiamjc06.pdf" } ], "resource_type": "article", "pub_year": "2006", "author_list": "Kempe, Julia; Kitaev, Alexei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3y99p-gqe61", "eprint_id": 3140, "eprint_status": "archive", "datestamp": "2023-08-22 05:08:44", "lastmod": "2023-10-16 15:39:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aharonov-D", "name": { "family": "Aharonov", "given": "Dorit" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" } } ] }, "title": "Fault-Tolerant Quantum Computation with Long-Range Correlated Noise", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum computing; quantum noise; fault tolerant computing", "note": "\u00a92006 The American Physical Society \n\n(Received 31 October 2005; published 7 February 2006) \n\nWe thank Daniel Gottesman for helpful comments. This work has been supported in part by DOE under Grant No. DE-FG03-92-ER40701, NSF under Grant No. PHY-0456720, ARO under Grants No. W911NF-04-1-0236, No. W911NF-05-1-0294, and No. DAAD19-00-1-0374, ISF under Grants No. 032-9739 and No. 039-7549, the U.S. Army under Grant No. 030-7657, and the Council of Higher Education in Israel under Grant No. 033-7233.", "abstract": "We prove a new version of the quantum accuracy threshold theorem that applies to non-Markovian noise with algebraically decaying spatial correlations. We consider noise in a quantum computer arising from a perturbation that acts collectively on pairs of qubits and on the environment, and we show that an arbitrarily long quantum computation can be executed with high reliability in D spatial dimensions, if the perturbation is sufficiently weak and decays with the distance r between the qubits faster than 1/r^D.", "date": "2006-02-10", "date_type": "published", "publication": "Physical Review Letters", "volume": "96", "number": "5", "publisher": "American Physical Society", "pagerange": "Art. No. 050504", "id_number": "CaltechAUTHORS:AHAprl06", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:AHAprl06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1103/PhysRevLett.96.050504", "primary_object": { "basename": "AHAprl06.pdf", "url": "https://authors.library.caltech.edu/records/3y99p-gqe61/files/AHAprl06.pdf" }, "resource_type": "article", "pub_year": "2006", "author_list": "Aharonov, Dorit; Kitaev, Alexei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wg6v4-ht550", "eprint_id": 2160, "eprint_status": "archive", "datestamp": "2023-08-22 04:58:49", "lastmod": "2023-10-13 23:14:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bonderson-P", "name": { "family": "Bonderson", "given": "Parsa" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Shtengel-K", "name": { "family": "Shtengel", "given": "Kirill" } } ] }, "title": "Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum Hall effect; interferometry; quasiparticles", "note": "\u00a92006 The American Physical Society \n\n(Received 30 August 2005; published 6 January 2006) \n\nThe authors would like to thank W. Bishara, N. Bonesteel, C. Chamon, J. Eisenstein, E. Fradkin, F. D. M. Haldane, S. Simon, N.-C. Yeh, and especially C. Nayak for many illuminating discussions. This work was supported in part by the NSF under Grant No. EIA-0086038 and the ARO under Grant No. W911NF-04-1-0236. K. S. would also like to acknowledge the hospitality of the Aspen Center for Physics.", "abstract": "In this Letter we propose an interferometric experiment to detect non-Abelian quasiparticle statistics\u2014one of the hallmark characteristics of the Moore-Read state expected to describe the observed fractional quantum Hall effect plateau at nu=5/2. The implications for using this state for constructing a topologically protected qubit as has been recently proposed by Das Sarma et al. are also addressed.", "date": "2006-01-13", "date_type": "published", "publication": "Physical Review Letters", "volume": "96", "number": "1", "publisher": "American Physical Society", "pagerange": "Art. No. 016803", "id_number": "CaltechAUTHORS:BONprl06.799", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BONprl06.799", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1103/PhysRevLett.96.016803", "primary_object": { "basename": "BONprl06.pdf", "url": "https://authors.library.caltech.edu/records/wg6v4-ht550/files/BONprl06.pdf" }, "resource_type": "article", "pub_year": "2006", "author_list": "Bonderson, Parsa; Kitaev, Alexei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zxskn-0rq20", "eprint_id": 2444, "eprint_status": "archive", "datestamp": "2023-08-22 04:51:20", "lastmod": "2023-10-13 23:24:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } } ] }, "title": "Anyons in an exactly solved model and beyond", "ispublished": "pub", "full_text_status": "public", "note": "Author preprint; arXiv.org/abs/cond-mat/0506438 \n\nDuring the years this work was in progress I received genuine interest and words of encouragement from John Preskill, Michael Freedman, Mikhail Feigelman, Grigory Volovik, and many other people. I thank Andreas Ludwig for having convinced me in the importance of the chiral central charge in the study of topological order. A conversation with Dmitri Ivanov was essential for understanding the difference between non-Abelian anyons and Majorana vortices in two-dimensional p-wave superconductors. I also thank Matthew Fisher, Nicholas Read, and Xiao-Gang Wen for helpful discussions. I am especially grateful to Jean Bellissard who read a preliminary version of the manuscript and made some valuable comments; in particular, he directed me to Ref. [50]. This work was supported in part by the National Science Foundation under Grant No. EIA-0086038 and by the Army Research Office under grant No. W911NF-04-1-0236. \n\nPublished article: \n\nAlexei Kitaev (2006) Anyons in an exactly solved model and beyond. Annals of Physics 321:2-111\n\nSubmitted - KITaop06.pdf
", "abstract": "A spin-1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z2 source gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are non-Abelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number \u03bd. The Abelian and non-Abelian phases of the original model correspond to \u03bd = 0 and \u03bd = \u00b11, respectively. The anyonic properties of excitation depend on \u03bd mod 16, whereas \u03bd itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.", "date": "2006-01", "date_type": "published", "publication": "Annals of Physics", "volume": "321", "number": "1", "publisher": "Elsevier", "pagerange": "2-111", "id_number": "CaltechAUTHORS:KITaop06", "issn": "0003-4916", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KITaop06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1016/j.aop.2005.10.005", "primary_object": { "basename": "KITaop06.pdf", "url": "https://authors.library.caltech.edu/records/zxskn-0rq20/files/KITaop06.pdf" }, "resource_type": "article", "pub_year": "2006", "author_list": "Kitaev, Alexei" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bmnrq-bc072", "eprint_id": 1172, "eprint_status": "archive", "datestamp": "2023-08-22 04:36:12", "lastmod": "2023-10-13 22:39:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Freedman-M-H", "name": { "family": "Freedman", "given": "Michael H." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Nayak-C", "name": { "family": "Nayak", "given": "Chetan" } }, { "id": "Slingerland-J-K", "name": { "family": "Slingerland", "given": "Johannes K." } }, { "id": "Walker-K", "name": { "family": "Walker", "given": "Kevin" } }, { "id": "Wang-Zhenghan", "name": { "family": "Wang", "given": "Zhenghan" }, "orcid": "0000-0002-5253-6400" } ] }, "title": "Universal manifold pairings and positivity", "ispublished": "pub", "full_text_status": "public", "keywords": "Manifold pairing, unitary, positivity, TQFT, s-cobordism", "note": "\u00a9 2005 Geometry & Topology Publications.\n\nSubmitted to G&T on 25 May 2005. (Revised 2 December 2005.) Paper accepted 3 December 2005. Paper published 10 December 2005.\n\nPublished - FREgt05.pdf
Submitted - 0503054v1.pdf
", "abstract": "Gluing two manifolds M_1 and M_2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x=Sum_i(a_i M_i) yields a sesquilinear pairing p=<,> with values in (formal linear combinations of) closed manifolds. Topological quantum field theory (TQFT) represents this universal pairing p onto a finite dimensional quotient pairing q with values in C which in physically motivated cases is positive definite. To see if such a \"unitary\" TQFT can potentially detect any nontrivial x, we ask if is non-zero whenever x is non-zero. If this is the case, we call the pairing p positive. The question arises for each dimension d=0,1,2,.... We find p(d) positive for d=0,1, and 2 and not positive for d=4. We conjecture that p(3) is also positive. Similar questions may be phrased for (manifold, submanifold) pairs and manifolds with other additional structure. The results in dimension 4 imply that unitary TQFTs cannot distinguish homotopy equivalent simply connected 4-manifolds, nor can they distinguish smoothly s-cobordant 4-manifolds. This may illuminate the difficulties that have been met by several authors in their attempts to formulate unitary TQFTs for d=3+1. There is a further physical implication of this paper. Whereas 3-dimensional Chern-Simons theory appears to be well-encoded within 2-dimensional quantum physics, eg in the fractional quantum Hall effect, Donaldson-Seiberg-Witten theory cannot be captured by a 3-dimensional quantum system. The positivity of the physical Hilbert spaces means they cannot see null vectors of the universal pairing; such vectors must map to zero.", "date": "2005-12-10", "date_type": "published", "publication": "Geometry and Topology", "volume": "9", "number": "53", "publisher": "Geometry & Topology Publications", "pagerange": "2303-2317", "id_number": "CaltechAUTHORS:FREgt05", "issn": "1465-3060", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:FREgt05", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.2140/gt.2005.9.2303", "primary_object": { "basename": "0503054v1.pdf", "url": "https://authors.library.caltech.edu/records/bmnrq-bc072/files/0503054v1.pdf" }, "related_objects": [ { "basename": "FREgt05.pdf", "url": "https://authors.library.caltech.edu/records/bmnrq-bc072/files/FREgt05.pdf" } ], "resource_type": "article", "pub_year": "2005", "author_list": "Freedman, Michael H.; Kitaev, Alexei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7w19k-px130", "eprint_id": 1053, "eprint_status": "archive", "datestamp": "2023-08-22 03:09:14", "lastmod": "2023-10-13 22:06:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bravyi-S", "name": { "family": "Bravyi", "given": "Sergey" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } } ] }, "title": "Universal quantum computation with ideal Clifford gates and noisy ancillas", "ispublished": "pub", "full_text_status": "public", "note": "\u00a92005 The American Physical Society \n\n(Received 6 May 2004; published 22 February 2005) \n\nWe thank Mikhail Vyalyi for bringing to our attention many useful facts about the Clifford group. This work has been supported in part by the National Science Foundation under Grant No. EIA-0086038.", "abstract": "We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis. In addition, we allow the creation of a one-qubit ancilla in a mixed state rho, which should be regarded as a parameter of the model. Our goal is to determine for which rho universal quantum computation (UQC) can be efficiently simulated. To answer this question, we construct purification protocols that consume several copies of rho and produce a single output qubit with higher polarization. The protocols allow one to increase the polarization only along certain \"magic\" directions. If the polarization of rho along a magic direction exceeds a threshold value (about 65%), the purification asymptotically yields a pure state, which we call a magic state. We show that the Clifford group operations combined with magic states preparation are sufficient for UQC. The connection of our results with the Gottesman-Knill theorem is discussed.", "date": "2005-02-01", "date_type": "published", "publication": "Physical Review A", "volume": "71", "number": "Art no", "publisher": "Physical Review A", "pagerange": "1-14", "id_number": "CaltechAUTHORS:BRApra05", "issn": "1050-2947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BRApra05", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1103/PhysRevA.71.022316", "primary_object": { "basename": "BRApra05.pdf", "url": "https://authors.library.caltech.edu/records/7w19k-px130/files/BRApra05.pdf" }, "resource_type": "article", "pub_year": "2005", "author_list": "Bravyi, Sergey and Kitaev, Alexei" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ym8rj-ydt09", "eprint_id": 3505, "eprint_status": "archive", "datestamp": "2023-08-22 01:54:18", "lastmod": "2023-10-16 15:57:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Mayers-D", "name": { "family": "Mayers", "given": "Dominic" } }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" } } ] }, "title": "Superselection rules and quantum protocols", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum cryptography; information theory; security of data; protocols; quantum computing", "note": "\u00a92004 The American Physical Society \n\n(Received 19 October 2003; published 21 May 2004) \n\nWe thank Stephen Bartlett, Michael Ben-Or, and Sandu Popescu for discussions. This work has been supported in part by the Department of Energy under Grant No. DEFG03-92-ER40701, by the National Science Foundation under Grant No. EIA-0086038, and by the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374.", "abstract": "We show that superselection rules do not enhance the information-theoretic security of quantum cryptographic protocols. Our analysis employs two quite different methods. The first method uses the concept of a reference system\u2014in a world subject to a superselection rule, unrestricted operations can be simulated by parties who share access to a reference system with suitable properties. By this method, we prove that if an n-party protocol is secure in a world subject to a superselection rule, then the security is maintained even if the superselection rule is relaxed. However, the proof applies only to a limited class of superselection rules, those in which the superselection sectors are labeled by unitary irreducible representations of a compact symmetry group. The second method uses the concept of the format of a message sent between parties\u2014by verifying the format, the recipient of a message can check whether the message could have been sent by a party who performed charge-conserving operations. By this method, we prove that protocols subject to general superselection rules (including those pertaining to non-Abelian anyons in two dimensions) are no more secure than protocols in the unrestricted world. However, the proof applies only to two-party protocols. Our results show in particular that, if no assumptions are made about the computational power of the cheater, then secure quantum bit commitment and strong quantum coin flipping with arbitrarily small bias are impossible in a world subject to superselection rules.", "date": "2004-05-01", "date_type": "published", "publication": "Physical Review A", "volume": "69", "number": "5", "publisher": "Physical Review A", "pagerange": "Art2. No. 052326", "id_number": "CaltechAUTHORS:KITpra04", "issn": "1050-2947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KITpra04", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1103/PhysRevA.69.052326", "primary_object": { "basename": "KITpra04.pdf", "url": "https://authors.library.caltech.edu/records/ym8rj-ydt09/files/KITpra04.pdf" }, "resource_type": "article", "pub_year": "2004", "author_list": "Kitaev, Alexei; Mayers, Dominic; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6nmmy-xhv73", "eprint_id": 99231, "eprint_status": "archive", "datestamp": "2023-08-19 12:50:11", "lastmod": "2024-01-14 21:59:41", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kempe-J", "name": { "family": "Kempe", "given": "Julia" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Regev-O", "name": { "family": "Regev", "given": "Oded" } } ] }, "title": "The Complexity of the Local Hamiltonian Problem", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2004 Springer-Verlag Berlin Heidelberg. \n\nDiscussions with Sergey Bravyi and Frank Verstraete are gratefully acknowledged. JK is supported by ACI S\u00e9curit\u00e9 Informatique, 2003-n24, projet \"R\u00e9seaux Quantiques\", ACI-CR 2002-40 and EU 5th framework program RESQ IST-2001-37559, and by DARPA and Air Force Laboratory, Air Force Materiel Command, USAF, under agreement number F30602-01-2-0524, and by DARPA and the\nOffice of Naval Research under grant number FDN-00014-01-1-0826 and during a visit supported in part by the National Science Foundation under grant EIA-0086038 through the Institute for Quantum Information at the California Institute of Technology. AK is supported in part by the National Science Foundation\nunder grant EIA-0086038. OR is supported by an Alon Fellowship and the Army Research Office grant DAAD19-03-1-0082. Part of this work was carried out during a visit of OR at LRI, Universit\u00e9 de Paris-Sud and he thanks his hosts for their hospitality and acknowledges partial support by ACI S\u00e9curit\u00e9 Informatique, 2003-n24, projet \"R\u00e9seaux Quantiques\".\n\nSubmitted - 0406180.pdf
", "abstract": "The k-Local Hamiltonian problem is a natural complete problem for the complexity class QMA, the quantum analog of NP. It is similar in spirit to MAX- k -SAT, which is NP-complete for k \u2265 2. It was known that the problem is QMA-complete for any k \u2265 3. On the other hand 1-Local Hamiltonian is in P, and hence not believed to be QMA-complete. The complexity of the 2-Local Hamiltonian problem has long been outstanding. Here we settle the question and show that it is QMA-complete. We provide two independent proofs; our first proof uses a powerful technique for analyzing the sum of two Hamiltonians; this technique is based on perturbation theory and we believe that it might prove useful elsewhere. The second proof uses elementary linear algebra only. Using our techniques we also show that adiabatic computation with two-local interactions on qubits is equivalent to standard quantum computation.", "date": "2004", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "372-383", "id_number": "CaltechAUTHORS:20191011-072647725", "isbn": "978-3-540-24058-7", "book_title": "FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191011-072647725", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "ACI S\u00e9curit\u00e9 Informatique", "grant_number": "ACI-CR 2002-40" }, { "agency": "European Union", "grant_number": "RESQ IST-2001-37559" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F30602-01-2-0524" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "FDN-00014-01-1-0826" }, { "agency": "NSF", "grant_number": "EIA-0086038" }, { "agency": "Tel-Aviv University" }, { "agency": "Army Research Office (ARO)", "grant_number": "DAAD19-03-1-0082" } ] }, "local_group": { "items": [ { "id": "IQIM" } ] }, "contributors": { "items": [ { "id": "Lodaya-K", "name": { "family": "Lodaya", "given": "Kamal" } }, { "id": "Mahajan-M", "name": { "family": "Mahajan", "given": "Meena" } } ] }, "doi": "10.1007/978-3-540-30538-5_31", "primary_object": { "basename": "0406180.pdf", "url": "https://authors.library.caltech.edu/records/6nmmy-xhv73/files/0406180.pdf" }, "resource_type": "book_section", "pub_year": "2004", "author_list": "Kempe, Julia; Kitaev, Alexei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/26c0z-18p29", "eprint_id": 2021, "eprint_status": "archive", "datestamp": "2023-08-22 00:36:04", "lastmod": "2023-10-13 23:09:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Vidal-G", "name": { "family": "Vidal", "given": "G." } }, { "id": "Latorre-J-I", "name": { "family": "Latorre", "given": "J. I." } }, { "id": "Rico-E", "name": { "family": "Rico", "given": "E." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A." } } ] }, "title": "Entanglement in Quantum Critical Phenomena", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum entanglement; critical points; conformal field theory; spin systems; long-range order; magnetic transitions", "note": "\u00a92003 The American Physical Society \n\n(Received 5 December 2002; published 2 June 2003) \n\nThis work was supported by the Spanish Grants No. GC2001SGR-00065 and No. MCYT FPA2001-3598, by the National Science Foundation of USA under Grant No. EIA\u20130086038, and by the European Union under Grant No. ISF1999-11053.", "abstract": "Entanglement, one of the most intriguing features of quantum theory and a main resource in quantum information science, is expected to play a crucial role also in the study of quantum phase transitions, where it is responsible for the appearance of long-range correlations. We investigate, through a microscopic calculation, the scaling properties of entanglement in spin chain systems, both near and at a quantum critical point. Our results establish a precise connection between concepts of quantum information, condensed matter physics, and quantum field theory, by showing that the behavior of critical entanglement in spin systems is analogous to that of entropy in conformal field theories. We explore some of the implications of this connection.", "date": "2003-06-06", "date_type": "published", "publication": "Physical Review Letters", "volume": "90", "number": "22", "publisher": "American Physical Society", "pagerange": "Art. No. 227902", "id_number": "CaltechAUTHORS:VIDprl03", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:VIDprl03", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1103/PhysRevLett.90.227902", "primary_object": { "basename": "VIDprl03.pdf", "url": "https://authors.library.caltech.edu/records/26c0z-18p29/files/VIDprl03.pdf" }, "resource_type": "article", "pub_year": "2003", "author_list": "Vidal, G.; Latorre, J. I.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b6es1-vp247", "eprint_id": 26604, "eprint_status": "archive", "datestamp": "2023-08-19 10:43:40", "lastmod": "2023-10-24 16:26:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A. Yu." } } ] }, "title": "Fault-tolerant quantum computation by anyons", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Elsevier Science. Received 20 May 2002; Available online 24 December 2002. I am grateful to J. Preskill, D.P. DiVincenzo and C.H. Bennett for interesting discussions\nand questions which helped me to clarify some points in my constructions. This work was supported, in part, by the Russian Foundation for Fundamental Research, Grant No. 96-01-01113. Part of this work was completed during the 1997\nElsag-Bailey\u2014I.S.I. Foundation research meeting on quantum computation.\n\nSubmitted - KITaop03preprint.pdf
", "abstract": "A two-dimensional quantum system with anyonic excitations can be considered as a quantum\ncomputer. Unitary transformations can be performed by moving the excitations around\neach other. Measurements can be performed by joining excitations in pairs and observing the\nresult of fusion. Such computation is fault-tolerant by its physical nature.", "date": "2003-01", "date_type": "published", "publication": "Annals of Physics", "volume": "303", "number": "1", "publisher": "Elsevier", "pagerange": "2-30", "id_number": "CaltechAUTHORS:20111005-144725727", "issn": "0003-4916", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111005-144725727", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Fundamental Research", "grant_number": "96-01-01113" } ] }, "doi": "10.1016/S0003-4916(02)00018-0", "primary_object": { "basename": "KITaop03preprint.pdf", "url": "https://authors.library.caltech.edu/records/b6es1-vp247/files/KITaop03preprint.pdf" }, "resource_type": "article", "pub_year": "2003", "author_list": "Kitaev, A. Yu." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kag81-nk917", "eprint_id": 1702, "eprint_status": "archive", "datestamp": "2023-08-21 23:40:41", "lastmod": "2023-10-13 22:57:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dennis-E", "name": { "family": "Dennis", "given": "Eric" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Landahl-A", "name": { "family": "Landahl", "given": "Andrew" } }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" } } ] }, "title": "Topological quantum memory", "ispublished": "pub", "full_text_status": "public", "keywords": "ERROR-CORRECTING CODES; ISING-MODEL; GROUND-STATES; 2 DIMENSIONS; COMPUTATION; GEOMETRY", "note": "Copyright \u00a9 2002 American Institute of Physics. \n\nReceived 25 October 2001; accepted 16 May 2002. \n\nWe happily acknowledge helpful discussions with many colleagues, including Dorit Aharonov, Charlie Bennett, Daniel Gottesman, Randy Kamien, Greg Kuperberg, Paul McFadden, Michael Nielsen, Peter Shor, Andrew Steane, Chenyang Wang, and Nathan Wozny. We are especially grateful to Peter Hoyer for discussions of efficient perfect matching algorithms. This work originated in 1997, while E.D. received support from Caltech's Summer Undergraduate Research Fellowship (SURF) program. This work has been supported in part by the Department of Energy under Grant No. DE-FG03-92-ER40701, by DARPA through the Quantum Information and Computation (QUIC) project administered by the Army Research Office under Grant No. DAAH04-96-1-0386, by the National Science Foundation under Grant No. EIA-0086038, by the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374, and by an IBM Faculty Partnership Award.", "abstract": "We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is below the critical value (the accuracy threshold), encoded information can be protected arbitrarily well in the limit of a large code block. This phase transition can be accurately modeled by a three-dimensional Z(2) lattice gauge theory with quenched disorder. We estimate the accuracy threshold, assuming that all quantum gates are local, that qubits can be measured rapidly, and that polynomial-size classical computations can be executed instantaneously. We also devise a robust recovery procedure that does not require measurement or fast classical processing; however, for this procedure the quantum gates are local only if the qubits are arranged in four or more spatial dimensions. We discuss procedures for encoding, measurement, and performing fault-tolerant universal quantum computation with surface codes, and argue that these codes provide a promising framework for quantum computing architectures.", "date": "2002-09-01", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "43", "number": "9", "publisher": "Journal of Mathematical Physics", "pagerange": "4452-4505", "id_number": "CaltechAUTHORS:DENjmp02.842", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:DENjmp02.842", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1063/1.1499754", "primary_object": { "basename": "DENjmp02.pdf", "url": "https://authors.library.caltech.edu/records/kag81-nk917/files/DENjmp02.pdf" }, "resource_type": "article", "pub_year": "2002", "author_list": "Dennis, Eric; Kitaev, Alexei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7mvw6-pzk76", "eprint_id": 27126, "eprint_status": "archive", "datestamp": "2023-08-19 09:32:55", "lastmod": "2023-10-24 16:53:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Freedman-M-H", "name": { "family": "Freedman", "given": "Michael H." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Wang-Zhenghan", "name": { "family": "Wang", "given": "Zhenghan" }, "orcid": "0000-0002-5253-6400" } ] }, "title": "Simulation of Topological Field Theories by Quantum Computers", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Springer-Verlag. \n\nReceived: 4 May 2001; Accepted: 16 January 2002. \n\nCommunicated by P. Sarnak. \n\nWe would like to thank Greg Kupperberg and Kevin Walker for many stimulating discussions on the material presented here.\n\nSubmitted - FREcmp02preprint.pdf
", "abstract": "Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned \"topological models\" having a finite dimensional internal state space with no natural tensor product structure and in which the evolution of the state is discrete, H \u2261 0. These are called topological quantum field theories (TQFTs). These exotic physical systems are proved to be efficiently simulated on a quantum computer. The conclusion is two-fold: \n1. TQFTs cannot be used to define a model of computation stronger than the usual quantum model \"BQP\".\n2. TQFTs provide a radically different way of looking at quantum computation. The rich mathematical structure of TQFTs might suggest a new quantum algorithm.", "date": "2002-06", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "227", "number": "3", "publisher": "Springer", "pagerange": "587-603", "id_number": "CaltechAUTHORS:20111007-112002181", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111007-112002181", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1007/s002200200635", "primary_object": { "basename": "FREcmp02preprint.pdf", "url": "https://authors.library.caltech.edu/records/7mvw6-pzk76/files/FREcmp02preprint.pdf" }, "resource_type": "article", "pub_year": "2002", "author_list": "Freedman, Michael H.; Kitaev, Alexei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ek9as-2p668", "eprint_id": 27125, "eprint_status": "archive", "datestamp": "2023-08-19 09:31:43", "lastmod": "2023-10-24 16:53:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bravyi-S-B", "name": { "family": "Bravyi", "given": "Sergey B." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei Yu." } } ] }, "title": "Fermionic Quantum Computation", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Elsevier Science.\nReceived March 6, 2002.\nAvailable online 11 June 2002.\n\nSubmitted - BRAaop02preprint.pdf
", "abstract": "We define a model of quantum computation with local fermionic modes (LFMs)\u2014sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m LFMs and the Hilbert space of m qubits, simulation of one fermionic gate takes O(m) qubit gates and vice versa. We show that using different encodings, the simulation cost can be reduced to O(log m) and a constant, respectively. Nearest neighbors fermionic gates on a graph of bounded degree can be simulated at a constant cost. A universal set of fermionic gates is found. We also study computation with Majorana fermions which are basically halves of LFMs. Some connection to qubit quantum codes is made.", "date": "2002-05-25", "date_type": "published", "publication": "Annals of Physics", "volume": "298", "number": "1", "publisher": "Elsevier", "pagerange": "210-226", "id_number": "CaltechAUTHORS:20111007-111528069", "issn": "0003-4916", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111007-111528069", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1006/aphy.2002.6254", "primary_object": { "basename": "BRAaop02preprint.pdf", "url": "https://authors.library.caltech.edu/records/ek9as-2p668/files/BRAaop02preprint.pdf" }, "resource_type": "article", "pub_year": "2002", "author_list": "Bravyi, Sergey B. and Kitaev, Alexei Yu." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4rebx-j5r09", "eprint_id": 1238, "eprint_status": "archive", "datestamp": "2023-08-21 23:09:01", "lastmod": "2023-10-13 22:41:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Beckman-D", "name": { "family": "Beckman", "given": "David" } }, { "id": "Gottesman-D", "name": { "family": "Gottesman", "given": "Daniel" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" } } ] }, "title": "Measurability of Wilson loop operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a92002 The American Physical Society \n\nReceived 23 October 2001; published 5 March 2002 \n\nWe thank Steve Giddings, Anton Kapustin, Michael Nielsen, Edward Witten, and especially Mark Srednicki for helpful discussions and comments. This work was supported in part by the Department of Energy under Grant No. DEFG03-92-ER40701, by the National Science Foundation under Grant No. EIA-0086038, by the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374, by IBM, and by the Clay Mathematics Institute. Some of this work was done at the Aspen Center for Physics.", "abstract": "We show that the nondemolition measurement of a spacelike Wilson loop operator W(C) is impossible in a relativistic non-Abelian gauge theory. In particular, if two spacelike-separated magnetic flux tubes both link with the loop C, then a nondemolition measurement of W(C) would cause electric charge to be transferred from one flux tube to the other, a violation of relativistic causality. A destructive measurement of W(C) is possible in a non-Abelian gauge theory with suitable matter content. In an Abelian gauge theory, many cooperating parties distributed along the loop C can perform a nondemolition measurement of the Wilson loop operator if they are equipped with a shared entangled ancilla that has been prepared in advance. We also note that Abelian electric charge (but not non-Abelian charge) can be transported superluminally, without any accompanying transmission of information.", "date": "2002-03-15", "date_type": "published", "publication": "Physical Review D", "volume": "65", "number": "6", "publisher": "Physical Review D", "pagerange": "Art. no. 065022", "id_number": "CaltechAUTHORS:BECprd02", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BECprd02", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1103/PhysRevD.65.065022", "primary_object": { "basename": "BECprd02.pdf", "url": "https://authors.library.caltech.edu/records/4rebx-j5r09/files/BECprd02.pdf" }, "resource_type": "article", "pub_year": "2002", "author_list": "Beckman, David; Gottesman, Daniel; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9pn21-d2z44", "eprint_id": 3849, "eprint_status": "archive", "datestamp": "2023-08-21 22:23:54", "lastmod": "2023-10-16 16:11:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gottesman-D", "name": { "family": "Gottesman", "given": "Daniel" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" } }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" } } ] }, "title": "Encoding a qubit in an oscillator", "ispublished": "pub", "full_text_status": "public", "note": "\u00a92001 The American Physical Society \n\nReceived 9 August 2000; published 11 June 2001 \n\nWe gratefully acknowledge helpful discussions with Isaac Chuang, Sumit Daftuar, David DiVincenzo, Andrew Doherty, Steven van Enk, Jim Harrington, Jeff Kimble, Andrew Landahl, Hideo Mabuchi, Harsh Mathur, Gerard Milburn, Michael Nielsen, and Peter Shor. This work was supported in part by the Department of Energy under Grant No. DE-FG03-92-ER40701, and by the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374. Some of this work was done at the Aspen Center for Physics.", "abstract": "Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum optics, fault-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a d-state system. Continuous-variable codes can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.", "date": "2001-07-01", "date_type": "published", "publication": "Physical Review A", "volume": "64", "number": "1", "publisher": "Physical Review A", "pagerange": "Art. No. 012310", "id_number": "CaltechAUTHORS:GOTpra01b", "issn": "1050-2947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GOTpra01b", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1103/PhysRevA.64.012310", "primary_object": { "basename": "GOTpra01b.pdf", "url": "https://authors.library.caltech.edu/records/9pn21-d2z44/files/GOTpra01b.pdf" }, "resource_type": "article", "pub_year": "2001", "author_list": "Gottesman, Daniel; Kitaev, Alexei; et el." } ]