Autoregressive neural Slater-Jastrow ansatz for variational Monte Carlo simulation

TL;DR

This paper introduces an autoregressive neural Slater-Jastrow ansatz for variational Monte Carlo that enables uncorrelated sampling with cubic scaling, improving efficiency in quantum simulations.

Contribution

It combines autoregressive neural networks with Slater determinants for the first time, enabling uncorrelated sampling and efficient energy calculations in variational Monte Carlo.

Findings

Achieved uncorrelated sampling in variational Monte Carlo.

Demonstrated cubic scaling of the algorithm with system size.

Benchmarked on the 2D t-V model of spinless fermions.

Abstract

Direct sampling from a Slater determinant is combined with an autoregressive deep neural network as a Jastrow factor into a fully autoregressive Slater-Jastrow ansatz for variational quantum Monte Carlo, which allows for uncorrelated sampling. The elimination of the autocorrelation time leads to a stochastic algorithm with provable cubic scaling (with a potentially large prefactor), i.e. the number of operations for producing an uncorrelated sample and for calculating the local energy scales like $\mathcal{O}(N_s^3)$ with the number of orbitals $N_s$. The implementation is benchmarked on the two-dimensional $t-V$ model of spinless fermions on the square lattice.