Digital quantum simulation of lattice fermion theories with local encoding

TL;DR

This paper proposes a scalable, platform-neutral digital quantum simulation method for lattice fermion theories using local encoding with auxiliary gauge fields, demonstrated through numerical emulation of Hubbard ladder dynamics.

Contribution

It introduces a novel local fermion encoding scheme with auxiliary gauge fields that enables scalable quantum simulation of lattice fermion theories.

Findings

Demonstrates a timescale separation for spin and charge excitations.

Shows the feasibility of simulating fermionic lattice theories with minimal gate requirements.

Validates the approach through numerical emulation of the Hubbard ladder.

Abstract

We numerically analyze the feasibility of a platform-neutral, general strategy to perform quantum simulations of fermionic lattice field theories under open boundary conditions. The digital quantum simulator requires solely one- and two-qubit gates and is scalable since integrating each Hamiltonian term requires a finite (non-scaling) cost. The exact local fermion encoding we adopt relies on auxiliary $\mathbb{Z}_2$ lattice gauge fields by adding a pure gauge Hamiltonian term akin to the Toric Code. By numerically emulating the quantum simulator real-time dynamics, we observe a timescale separation for spin- and charge-excitations in a spin-$\frac{1}{2}$ Hubbard ladder in the $t-J$ model limit.