Evaluating Machine Learning Approaches for Discovering Optimal Sets of Projection Operators for Quantum State Tomography of Qubit Systems

Finding optimal measurement schemes in quantum state tomography is a fundamental problem in quantum computation. It is known that for non-degenerate operators the optimal measurement scheme is based on mutually unbiassed bases. This paper is a follow up from our previous work, where we use standard numerical approaches to look for optimal measurement schemes, where the measurement operators are projections on individual pure quantum states. In this paper we demonstrate the usefulness of several machine learning techniques – reinforcement learning and parallel machine learning approaches, to discover measurement schemes, which are significantly better than the ones discovered by standard numerical methods in our previous work. The high-performing quorums of projection operators we have discovered have complex structure and symmetries, which may imply that the optimal solution will possess such symmetries.