Quantum Ground States from Reinforcement Learning*

The past few years have seen numerous attempts to leverage the power of deep networks to solve the quantum many-body problem, and neural representations of many body wavefunctions have proliferated. However, there are several mathematically equivalent formulations of quantum mechanics, and hence alternative routes for the application of machine learning.

We demonstrate how reinforcement learning may be used to solve problems in quantum systems via the path integral representation. Our work provides a novel neural approach to many-body quantum mechanics that leverages optimal control to approximate the Feynman–Kac path measure. The drift of the quantum stochastic control process is chosen to match the distribution of paths in the Feynman–Kac representation of the solution of the imaginary time Schrodinger equation. This provides a variational principle that can be used for reinforcement learning of a neural representation and a new alternative to prior deep learning approaches that start from the Schrodinger picture. Further, our approach learns an optimal importance sampler for the FK trajectories, providing a drop-in replacement for path integral Monte Carlo.