Ground States of Quantum Many Body Lattice Models via Reinforcement Learning
arXiv:2012.07063
Abstract
We introduce reinforcement learning (RL) formulations of the problem of finding the ground state of a many-body quantum mechanical model defined on a lattice. We show that stoquastic Hamiltonians - those without a sign problem - have a natural decomposition into stochastic dynamics and a potential representing a reward function. The mapping to RL is developed for both continuous and discrete time, based on a generalized Feynman-Kac formula in the former case and a stochastic representation of the Schrödinger equation in the latter. We discuss the application of this mapping to the neural representation of quantum states, spelling out the advantages over approaches based on direct representation of the wavefunction of the system.
arXiv commentAccepted at MSML2021
References in corpus (11)
- Adam: A Method for Stochastic Optimization
- Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- Reinforcement Learning with Deep Energy-Based Policies
- Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review
- Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
- Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
- Solving Many-Electron Schrödinger Equation Using Deep Neural Networks
- Soft Actor-Critic for Discrete Action Settings
- Information asymmetry in KL-regularized RL
- Monte Carlo simulation of stoquastic Hamiltonians