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arXiv:2210.16493

Neural network quantum state with proximal optimization: a ground-state searching scheme based on variational Monte Carlo

Feng Chen, Ming Xue

Published Oct 29, 2022• 0 citations
arXivHTMLPDF

Abstract

Neural network quantum states (NQS), incorporating with variational Monte Carlo (VMC) method, are shown to be a promising way to investigate quantum many-body physics. Whereas vanilla VMC methods perform one gradient update per sample, we introduce a novel objective function with proximal optimization (PO) that enables multiple updates via reusing the mismatched samples. Our VMC-PO method keeps the advantage of the previous importance sampling gradient optimization algorithm [L. Yang, {\it et al}, Phys. Rev. Research {\bf 2}, 012039(R)(2020)] that efficiently uses sampled states. PO mitigates the numerical instabilities during network updates, which is similar to stochastic reconfiguration (SR) methods, but achieves an alternative and simpler implement with lower computational complexity. We investigate the performance of our VMC-PO algorithm for ground-state searching with a 1-dimensional transverse-field Ising model and 2-dimensional Heisenberg antiferromagnet on a square lattice, and demonstrate that the reached ground-state energies are comparable to state-of-the-art results.

DOI
10.48550/arxiv.2210.16493

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Variational Monte Carlo (VMC) is an approach for computing ground-state wave functions that has recently become more powerful due to the introduction of neural network-based wave-function parametrizations. However, efficiently training neural wave functions to converge to an energy minimum remains a difficult problem. In this work, we analyze optimization and sampling methods used in VMC and introduce alterations to improve their performance. First, based on theoretical convergence analysis in a noiseless setting, we motivate a new optimizer that we call the Rayleigh-Gauss-Newton method, which can improve upon gradient descent and natural gradient descent to achieve superlinear convergence at no more than twice the computational cost. Second, to realize this favorable comparison in the presence of stochastic noise, we analyze the effect of sampling error on VMC parameter updates and experimentally demonstrate that it can be reduced by the parallel tempering method. In particular, we demonstrate that RGN can be made robust to energy spikes that occur when the sampler moves between metastable regions of configuration space. Finally, putting theory into practice, we apply our enhanced optimization and sampling methods to the transverse-field Ising and XXZXXZXXZ models on large lattices, yielding ground-state energy estimates with remarkably high accuracy after just 200 parameter updates.