Solving the quantum many-body problem with artificial neural networks

TLDR

The quantum many‑body problem is difficult because the wave function’s exponential complexity encodes non‑trivial correlations. The authors aim to use machine learning to represent quantum states with neural networks, thereby reducing the many‑body wave function’s complexity to a tractable form. They employ a variational neural‑network ansatz with a reinforcement‑learning scheme to find ground states or simulate unitary dynamics of interacting quantum systems. The approach achieves high accuracy for equilibrium and dynamical properties of one‑ and two‑dimensional spin models, proving its effectiveness for solving the quantum many‑body problem.

Abstract

The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the non-trivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that systematic machine learning of the wave function can reduce this complexity to a tractable computational form, for some notable cases of physical interest. We introduce a variational representation of quantum states based on artificial neural networks with variable number of hidden neurons. A reinforcement-learning scheme is then demonstrated, capable of either finding the ground-state or describing the unitary time evolution of complex interacting quantum systems. We show that this approach achieves very high accuracy in the description of equilibrium and dynamical properties of prototypical interacting spins models in both one and two dimensions, thus offering a new powerful tool to solve the quantum many-body problem.