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.

翻译：本文重新审视了量子态层析成像中密度矩阵估计问题的伪贝叶斯方法。研究表明，伪贝叶斯推断为量子层析成像提供了强大的范式，并取得了引人注目的理论和实证结果。然而，由于需要从复杂高维分布中采样，伪贝叶斯估计量的计算面临显著挑战，这限制了其在实际场景中的应用。为解决这一问题，我们针对伪贝叶斯估计量提出了一种高效的自适应MCMC采样方法。仿真结果表明，与先前实现相比，我们的方法速度提升至少两个数量级，这对实际量子层析成像具有重要意义。