Classical Simulation of Boson Sampling Based on Graph Structure

Oh, Changhun; Lim, Youngrong; Fefferman, Bill; Jiang, Liang

doi:10.1103/physrevlett.128.190501

Cited by 22 publications

(25 citation statements)

References 44 publications

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“…Permanent and hafnian are important matrix functions in computational complexity. Although computing these matrix functions is generally hard [20,27,28], there are still efficient methods for matrices that have specific structures or restrictions [29][30][31][32]. Developing algorithms for estimating matrix functions of particular classes of matrices is a highly nontrivial problem and might enable us to understand the hardness of the problem better.…”

Section: B Manipulating Quasiprobability In the Phase Spacementioning

confidence: 99%

Approximating outcome probabilities of linear optical circuits

Lim

2023

Preprint

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Quasiprobability representation is an important tool for analyzing a quantum system, such as a quantum state or a quantum circuit. In this work, we propose classical algorithms specialized for approximating outcome probabilities of a linear optical circuit using $s$-parameterized quasiprobability distributions. Notably, we can reduce the negativity bound of a circuit from exponential to at most polynomial for specific cases by modulating the shapes of quasiprobability distributions thanks to the symmetry of the linear optical transformation in the phase space. Consequently, our scheme renders an efficient estimation of outcome probabilities within an additive error whose precision depends on the classicality of the circuit. When the classicality is high enough, we reach a polynomial-time estimation algorithm of a probability within a multiplicative error by an efficient sampling from the log-concave function. By choosing appropriate input states and measurements, our results provide plenty of quantum-inspired classical algorithms for approximating various matrix functions beating best-known results. Moreover, we give sufficient conditions for the classical simulability of Gaussian boson sampling using the approximating algorithm for any (marginal) outcome probability under the poly-sparse condition.

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Section: B Manipulating Quasiprobability In the Phase Spacementioning

confidence: 99%

Approximating outcome probabilities of linear optical circuits

Lim

2023

Preprint

Self Cite

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“…As a result, proposed schemes of improvement generally avoid high-depth optical circuits while trying to maintain high connectivity between optical modes [27,28]. Although carving out a small regime under which approximate sampling is hard to simulate, these schemes limit the experiments, potential algorithms that can be performed, and most importantly, the complexity [43,44]. Additional investigations are necessary for understanding the effect of loss on the asymptotic complexity of proposed quantum algorithms for scalable quantum supremacy demonstration.…”

Section: Introductionmentioning

confidence: 99%

Complexity of Gaussian boson sampling with tensor networks

Liu¹,

Oh²,

Liu³

et al. 2023

Preprint

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“…In this work, we demonstrate that optimized numerical estimators can still be statistically more accurate than analytical ones when quantum circuits are subjected to noise channels, which is part of a crucial research topic that is intimately related to the possibility of a quantum advantage using noisy circuits, especially when the qubit number is large [72][73][74][75][76][77][78][79][80][81][82][83][84][85]. After recalling the concepts of gradient and Hessian estimation in Sec.…”

Section: Introductionmentioning

confidence: 99%

Optimized numerical gradient and Hessian estimation for variational quantum algorithms

Teo

2023

Phys. Rev. A

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With a finite amount of measurement data acquired in variational quantum algorithms, the statistical benefits of several optimized numerical estimation schemes, including the scaled parameter-shift (SPS) rule and finite-difference (FD) method, for estimating gradient and Hessian functions over analytical schemes [unscaled parameter-shift (PS) rule] were reported by the present author in [Y. S. Teo, Phys. Rev. A 107, 042421 (2023)]. We continue the saga by exploring the extent to which these numerical schemes remain statistically more accurate for a given number of sampling copies in the presence of noise. For noise-channel error terms that are independent of the circuit parameters, we demonstrate that without any knowledge about the noise channel, using the SPS and FD estimators optimized specifically for noiseless circuits can still give lower mean-squared errors than PS estimators for substantially wide sampling-copy number ranges-specifically for SPS, closed-form meansquared error expressions reveal that these ranges grow exponentially in the qubit number and reciprocally with a decreasing error rate. Simulations also demonstrate similar characteristics for the FD scheme. Lastly, if the error rate is known, we propose a noise-model-agnostic error-mitigation procedure to optimize the SPS estimators under the assumptions of two-design circuits and circuit-parameter-independent noise-channel error terms. We show that these heuristically-optimized SPS estimators can significantly reduce mean-squared-error biases that naive SPS estimators possess even with realistic circuits and noise channels, thereby improving their estimation qualities even further. The heuristically-optimized FD estimators possess as much mean-squared-error biases as the naively-optimized counterparts, and are thus not beneficial with noisy circuits.

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Classical Simulation of Boson Sampling Based on Graph Structure

Cited by 22 publications

References 44 publications

Approximating outcome probabilities of linear optical circuits

Approximating outcome probabilities of linear optical circuits

Complexity of Gaussian boson sampling with tensor networks

Optimized numerical gradient and Hessian estimation for variational quantum algorithms

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