Unbiasing Fermionic Auxiliary-Field Quantum Monte Carlo with Matrix Product State Trial Wavefunctions

TL;DR

This paper introduces MPS-AFQMC, a novel method combining matrix product state trial wavefunctions with fermionic auxiliary-field quantum Monte Carlo, enabling improved electronic structure calculations.

Contribution

The work presents the first implementation of MPS-AFQMC, including new heuristics and techniques for efficient energy evaluation, expanding the capabilities of quantum Monte Carlo methods.

Findings

Successfully improved fermionic phaseless AFQMC energies

Developed matrix product state overlap and energy evaluation methods

Demonstrated utility on hydrogen lattice systems

Abstract

In this work, we report, for the first time, an implementation of fermionic auxiliary-field quantum Monte Carlo (AFQMC) using matrix product state (MPS) trial wavefunctions, dubbed MPS-AFQMC. Calculating overlaps between an MPS trial and arbitrary Slater determinants up to a multiplicative error, a crucial subroutine in MPS-AFQMC, is proven to be #P-hard. Nonetheless, we tested several promising heuristics in successfully improving fermionic phaseless AFQMC energies. We also proposed a way to evaluate local energy and force bias evaluations free of matrix product operators. This allows for larger basis set calculations without significant overhead. We showcase the utility of our approach on one- and two-dimensional hydrogen lattices, even when the MPS trial itself struggles to obtain high accuracy. Our work offers a new set of tools that can solve currently challenging electronic structure problems with future improvements.