Truncation uncertainties for accurate quantum simulations of lattice gauge theories

TL;DR

This paper develops a formalism to estimate truncation errors in quantum simulations of lattice gauge theories, significantly improving previous error bounds by many orders of magnitude.

Contribution

It introduces a new method for estimating truncation errors in the electric basis, enhancing accuracy in quantum lattice gauge theory simulations.

Findings

Truncation error decreases factorially with field truncation size.

Applied formalism to Schwinger model and U(1) gauge theory.

Achieved error estimates improved by a factor of 10^{306}.

Abstract

The encoding of lattice gauge theories onto quantum computers requires a discretization of the gauge field's Hilbert space on each link, which presents errors with respect to the Kogut--Susskind limit. In the electric basis, Hilbert space fragmentation has recently been shown to limit the excitation of large electric fields. Here, we leverage this to develop a formalism for estimating the size of truncation errors in the electric basis. Generically, the truncation error falls off as a factorial of the field truncation. Examples of this formalism are applied to the Schwinger model and a pure U(1) lattice gauge theory. For reasonable choices of parameters, we improve on previous error estimates by a factor of 10^{306}.