Numerical comparison of MCMC methods for Quantum Tomography

Details

Supervisors

Massart, Estelle ; Andrew Thompson

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

Quantum Tomography is a process to reconstruct the state of a quantum system. By measuring replicas of the state, we can estimate the density matrix that represents it. Many methods exist to approximate the density matrix, including direct and optimization-based approaches. In recent years, however, Bayesian methods have emerged as a promising alternative thanks to their ability to incorporate prior information and quantify uncertainty. In this work, our contribution is twofold. First, we numerically compare 2 recent MCMC methods, the prob-estimator, and the Projected Langevin algorithm, in different experimental setups. Second, we introduce 2 new algorithms that combine the prior used in Projected Langevin with the algorithm from the prob-estimator. This allows us to evaluate the advantages that a gradient-based method brings, as well as the impact of a Student-t prior on the result.