Entanglement Features of Random Neural Network Quantum States

Abstract

Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin states encoded by random RBMs with independent and identically distributed complex Gaussian weights. By mapping the computation of ensemble-averaged quantities to statistical mechanics models, we are able to investigate the parameter space of the RBM ensemble in the thermodynamic limit. We discover qualitatively distinct wave functions by varying RBM parameters, which correspond to distinct phases in the equivalent statistical mechanics model. Notably, there is a regime in which the typical RBM states have near-maximal entanglement entropy in the thermodynamic limit, similar to that of Haar-random states. However, these states generically exhibit nonergodic behavior in the Ising basis, and do not form quantum state designs, making them distinguishable from Haar-random states.

22 pages, 13 figures, close to published version

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• Improving neural network performance for solving quantum sign structure
• Investigating Stark many-body localization with continuous unitary transformation flows
• Bound on entanglement in neural quantum states
• An Empirical Study of Quantum Dynamics as a Ground State Problem with Neural Quantum States
• Threshold (Q, P) Quantum Distillation