Obtaining continuum physics from dynamical simulations of Hamiltonian lattice gauge theories

TL;DR

This paper introduces the SBTE protocol, a new framework for controlling errors from approximate time evolution in quantum lattice gauge theory simulations, ensuring accurate continuum limits and enabling fair comparisons of algorithms.

Contribution

The paper proposes the SBTE protocol, a rigorous method to manage systematic errors from approximate evolution, improving continuum limit extraction in lattice gauge theory simulations.

Findings

SBTE protocol effectively controls evolution errors below statistical uncertainties.

Guarantees that approximate evolution errors do not affect the continuum limit.

Simplifies renormalization procedures for lattice gauge theory simulations.

Abstract

Taking the continuum limit is essential for extracting physical observables from quantum simulations of lattice gauge theories. Achieving the correct continuum limit requires careful control of all systematic uncertainties, including those arising from approximate implementations of the time evolution operator. In this work, we review existing approaches based on renormalization techniques, and point out their limitations. To overcome these limitations, we introduce a new general framework -- the Statistically-Bounded Time Evolution (SBTE) protocol -- for rigorously controlling the impact of approximate time evolution on the continuum limit. The central insight is that, since exact time evolution introduces no UV divergences, errors from approximate evolution can be treated as a source of systematic uncertainty that can be neglected if reduced below the working statistical uncertainty. We show that, using the SBTE protocol, which prescribes driving the approximate time evolution error below the working statistical uncertainty, leads to a simplified renormalization procedure. Furthermore, we show that, due to the existence of rigorous error bounds, one can guarantee a priori that such errors are negligible and do not affect the continuum limit. Ultimately, our protocol lays the foundation for performing systematic and fair comparisons between different simulation algorithms for lattice gauge theory simulations.