An efficient adaptive MCMC algorithm for Pseudo-Bayesian quantum tomography
arXiv:2106.00577 · doi:10.1007/s00180-022-01264-x
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.
References in corpus (9)
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- A practical and efficient approach for Bayesian quantum state estimation
- On the properties of variational approximations of Gibbs posteriors
- Rank-based model selection for multiple ions quantum tomography
- Monte Carlo sampling from the quantum state space. II
- A Bayesian Approach for Noisy Matrix Completion: Optimal Rate under General Sampling Distribution
- Quantum Model Averaging
- Quantum state tomography: Mean squared error matters, bias does not
- Efficient Bayesian reduced rank regression using Langevin Monte Carlo approach