Reinforcement Learning with Neural Networks for Quantum Multiple Hypothesis Testing

TL;DR

This paper applies reinforcement learning with neural networks to quantum hypothesis testing, successfully finding locally adaptive measurement strategies for multiple qubit states, and explores the gap between local and collective measurement optimality.

Contribution

It introduces RLNN for designing feasible local measurement strategies in quantum hypothesis testing and analyzes the gap between local and collective measurement optimality.

Findings

RLNN finds optimal local measurement strategies for up to 20 qubits.

RLNN strategies outperform locally greedy approaches in success probability.

Significant gap identified between local and collective measurement efficiencies.

Abstract

Reinforcement learning with neural networks (RLNN) has recently demonstrated great promise for many problems, including some problems in quantum information theory. In this work, we apply RLNN to quantum hypothesis testing and determine the optimal measurement strategy for distinguishing between multiple quantum states $\{ \rho_{j} \}$ while minimizing the error probability. In the case where the candidate states correspond to a quantum system with many qubit subsystems, implementing the optimal measurement on the entire system is experimentally infeasible. We use RLNN to find locally-adaptive measurement strategies that are experimentally feasible, where only one quantum subsystem is measured in each round. We provide numerical results which demonstrate that RLNN successfully finds the optimal local approach, even for candidate states up to 20 subsystems. We additionally demonstrate that the RLNN strategy meets or exceeds the success probability for a modified locally greedy approach in each random trial. While the use of RLNN is highly successful for designing adaptive local measurement strategies, in general a significant gap can exist between the success probability of the optimal locally-adaptive measurement strategy and the optimal collective measurement. We build on previous work to provide a set of necessary and sufficient conditions for collective protocols to strictly outperform locally adaptive protocols. We also provide a new example which, to our knowledge, is the simplest known state set exhibiting a significant gap between local and collective protocols. This result raises interesting new questions about the gap between theoretically optimal measurement strategies and practically implementable measurement strategies.