Abstract: Stabilized cat qubits that possess biased noise channel with bit-flip errors exponentially smaller than phase-flip errors. Together with a set of bias-preserving (BP) gates, cat qubits are a promising candidate for realizing hardware efficient quantum error correction and fault-tolerant quantum computing. Compared to dissipatively stabilized cat qubits, the Kerr cat qubits can in principle support faster gate operations with higher gate fidelity, benefiting from the large energy gap that protects the code space. However, the leakage of the Kerr cats can increase the minor type of errors and compromise the noise bias. Both the fast implementation of gates and the interaction with environment can lead to such detrimental leakage if no sophisticated controls are applied. In this work, we introduce new fine-control techniques to overcome the above obstacles for Kerr cat qubits. To suppress the gate leakage, we use the derivative-based transition suppression technique to design derivative-based controls for the Kerr BP gates. We show that the fine-controlled gates can simultaneously have high gate fidelity and high noise bias and when applied to concatenated quantum error correction, can not only improve the logical error rate but also reduce resource overhead. To suppress the environment-induced leakage, we introduce colored single-photon dissipation, which can continuously cool the Kerr cats and suppress the minor errors while not enhancing the major errors.

No.: 12015
ID: CaltechAUTHORS:20220307-189714000

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Abstract: The work concerns the problem of finding a protocol for randomness amplification secure against non-signaling adversary with polynomial number of devices, which allows for correlations between the device and the source of weak randomness. We focus on the epsilon-Santha-Vazirani sources, and provide two results in this direction. First we revisit the seminal protocol of R. Colbeck and R. Renner (CR protocol) of randomness amplification using Santha-Vazirani (SV) sources, and prove its security relaxing partially assumptions of independence between the devices and the source at a price of narrowed range of epsilon. The relaxation allows that the SV source can indicate as a final device from which randomness is taken choosen with uniform probability from the insecure devices. The proof of relaxation bases on the assumption which is a generalization of Santha-Vazirani condition - the SV condition for boxes: there does not exist a device such that given its inputs and outputs one can get to know the value of SV source by more than epsilon. Second, we prove security of the CR protocol allowing arbitrary correlations between SV source and device, up to the mentioned SV-box condition, and the assumption that the devices are not correlated with each other. We prove that if the final device chosen in the protocol was not secure, an independent tester could guess the value of SV source bits more than the SV-box condition allows. The strategy of a tester is to choose a random device out of the ones which do not satisfy condition of the Chain Bell inequality. The idea of the proof of the second result indicates that the CR protocol may be secure under attack which arbitrarily correlates SV with devices of arbitrary type, and is promising in studying this problem.

No.: 10442
ID: CaltechAUTHORS:20190827-110541191

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Abstract: We give a quantum algorithm for solving semidefinite programs (SDPs). It has worst-case running time n^(1/2) m^(1/2) s^2 poly(log(n), log(m), R, r, 1/δ), with n and s the dimension and row-sparsity of the input matrices, respectively, m the number of constraints, δ the accuracy of the solution, and R, r upper bounds on the size of the optimal primal and dual solutions, respectively. This gives a square-root unconditional speed-up over any classical method for solving SDPs both in n and m. We prove the algorithm cannot be substantially improved (in terms of n and m) giving a Ω(n^(1/2) + m^2) quantum lower bound for solving semidefinite programs with constant s, R, r and δ. The quantum algorithm is constructed by a combination of quantum Gibbs sampling and the multiplicative weight method. In particular it is based on a classical algorithm of Arora and Kale for approximately solving SDPs. We present a modification of their algorithm to eliminate the need for solving an inner linear program which may be of independent interest.

ID: CaltechAUTHORS:20180105-142517243

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Abstract: Recall the classical hypothesis testing setting with two convex sets of probability distributions P and Q. One receives either n i.i.d. samples from a distribution p ∈ P or from a distribution q ∈ Q and wants to decide from which set the points were sampled. It is known that the optimal exponential rate at which errors decrease can be achieved by a simple maximum-likelihood ratio test which does not depend on p or q, but only on the sets P and Q. We consider an adaptive generalization of this model where the choice of p ∈ P and q ∈ Q can change in each sample in some way that depends arbitrarily on the previous samples. In other words, in the kth round, an adversary, having observed all the previous samples in rounds 1, ..., κ-1, chooses p_κ ∈ P and q_κ ∈ Q, with the goal of confusing the hypothesis test. We prove that even in this case, the optimal exponential error rate can be achieved by a simple maximum-likelihood test that depends only on P and Q. We then show that the adversarial model has applications in hypothesis testing for quantum states using restricted measurements. For example, it can be used to study the problem of distinguishing entangled states from the set of all separable states using only measurements that can be implemented with local operations and classical communication (LOCC). The basic idea is that in our setup, the deleterious effects of entanglement can be simulated by an adaptive classical adversary. We prove a quantum Stein's Lemma in this setting: In many circumstances, the optimal hypothesis testing rate is equal to an appropriate notion of quantum relative entropy between two states. In particular, our arguments yield an alternate proof of Li and Winter's recent strengthening of strong subadditivity for quantum relative entropy.

ID: CaltechAUTHORS:20200730-074813402

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