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Variational Monte Carlo (VMC) is an approach for computing ground-statewavefunctions that has recently become more powerful due to the introduction ofneural network-based wavefunction parametrizations. However, efficientlytraining neural wavefunctions to converge to an energy minimum remains adifficult problem. In this work, we analyze optimization and sampling methodsused in VMC and introduce alterations to improve their performance. First,based on theoretical convergence analysis in a noiseless setting, we motivate anew optimizer that we call the Rayleigh-Gauss-Newton method, which can improveupon gradient descent and natural gradient descent to achieve superlinearconvergence at no more than twice the computational cost. Second, in order torealize this favorable comparison in the presence of stochastic noise, weanalyze the effect of sampling error on VMC parameter updates andexperimentally demonstrate that it can be reduced by the parallel temperingmethod. In particular, we demonstrate that RGN can be made robust to energyspikes that occur when the sampler moves between metastable regions ofconfiguration space. Finally, putting theory into practice, we apply ourenhanced optimization and sampling methods to the transverse-field Ising andXXZ models on large lattices, yielding ground-state energy estimates withremarkably high accuracy after just 200 parameter updates.

Rayleigh-Gauss-Newton optimization with enhanced sampling for variational Monte Carlo