Variational solutions to fermion-to-qubit mappings in two spatial dimensions

TL;DR

This paper introduces a variational Monte Carlo approach for studying 2D fermionic systems using higher-dimensional Jordan-Wigner transformations, effectively handling constraints and enabling analysis with neural network quantum states.

Contribution

It develops a novel variational framework that addresses constraints in fermion-to-qubit mappings in two dimensions, integrating neural network ansatze for ground and excited states.

Findings

Successfully solves parity and Gauss-law constraints.

Retrieves ground state and excitation spectra of the 2D $t$-$V$ model.

Demonstrates effectiveness of neural network quantum states in this context.

Abstract

Through the introduction of auxiliary fermions, or an enlarged spin space, one can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional constraints. We present a variational Monte-Carlo framework to study fermionic systems through higher-dimensional (>1D) Jordan-Wigner transformations. We provide exact solutions to the parity and Gauss-law constraints that are encountered in bosonization procedures. We study the $t$-$V$ model in 2D and demonstrate how both the ground state and the low-energy excitation spectra can be retrieved in combination with neural network quantum state ansatze.