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An efficient adaptive MCMC algorithm for Pseudo-Bayesian quantum tomography

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  • The Tien Mai

    (Norwegian University of Science and Technology)

Abstract

We revisit the Pseudo-Bayesian approach to the problem of estimating density matrix in quantum state tomography in this paper. Pseudo-Bayesian inference has been shown to offer a powerful paradigm for quantum tomography with attractive theoretical and empirical results. However, the computation of (Pseudo-)Bayesian estimators, due to sampling from complex and high-dimensional distribution, pose significant challenges that hamper their usages in practical settings. To overcome this problem, we present an efficient adaptive MCMC sampling method for the Pseudo-Bayesian estimator by exploring an adaptive proposal scheme together with subsampling method. We show in simulations that our approach is substantially computationally faster than the previous implementation by at least two orders of magnitude which is significant for practical quantum tomography.

Suggested Citation

  • The Tien Mai, 2023. "An efficient adaptive MCMC algorithm for Pseudo-Bayesian quantum tomography," Computational Statistics, Springer, vol. 38(2), pages 827-843, June.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:2:d:10.1007_s00180-022-01264-x
    DOI: 10.1007/s00180-022-01264-x
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    References listed on IDEAS

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    1. D. S. Gonçalves & C. L. N. Azevedo & C. Lavor & M. A. Gomes-Ruggiero, 2018. "Bayesian inference for quantum state tomography," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(10), pages 1846-1871, July.
    2. P. G. Bissiri & C. C. Holmes & S. G. Walker, 2016. "A general framework for updating belief distributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 1103-1130, November.
    3. L. M. Artiles & R. D. Gill & M. I. Gut¸ă, 2005. "An invitation to quantum tomography," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 109-134, February.
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