Ground States of Quantum Many Body Lattice Models via Reinforcement Learning

• URL: http://arxiv.org/abs/2012.07063v2
• Date: Sun, 11 Apr 2021 11:31:19 GMT
• Title: Ground States of Quantum Many Body Lattice Models via Reinforcement Learning
• Authors: Willem Gispen and Austen Lamacraft
• Abstract summary: We introduce reinforcement learning (RL) formulations of the problem of finding the ground state of a quantum mechanical model defined on a lattice. We show that stoquastic Hamiltonians have a natural decomposition into dynamics and a potential representing a reward function. 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 Schr\"odinger 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.

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