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

摘要

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