Quantum Ground States from Reinforcement Learning

Abstract

Finding the ground state of a quantum mechanical system can be formulated as an optimal control problem. In this formulation, the drift of the optimally controlled process is chosen to match the distribution of paths in the Feynman–Kac (FK) representation of the solution of the imaginary time Schrödinger equation. This provides a variational principle that can be used for reinforcement learning of a neural representation of the drift. Our approach is a drop-in replacement for path integral Monte Carlo, learning an optimal importance sampler for the FK trajectories. We demonstrate the applicability of our approach to several problems of one-, two-, and many-particle physics.