An efficient adaptive MCMC algorithm for Pseudo-Bayesian quantum tomography

TL;DR

This paper introduces an efficient adaptive MCMC algorithm that significantly accelerates Pseudo-Bayesian quantum state tomography, making it more practical for real-world applications by addressing computational challenges.

Contribution

The paper proposes a novel adaptive MCMC sampling method that greatly improves the computational efficiency of Pseudo-Bayesian quantum tomography estimators.

Findings

Our method is at least 100 times faster than previous implementations.

The approach maintains accuracy while reducing computation time.

Simulations demonstrate practical feasibility for quantum state estimation.

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 paradign 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 hampers their usages in practical settings. To overcome this problem, we present an efficient adaptive MCMC sampling method for the Pseudo-Bayesian estimator. We show in simulations that our approach is substantially faster than the previous implementation by at least two orders of magnitude which is significant for practical quantum tomography.