Trade-offs in Gauss's law error correction for lattice gauge theory quantum simulations

TL;DR

This paper investigates the limitations of Gauss's law-based quantum error correction in lattice gauge theory simulations, revealing trade-offs between error correction benefits and constraints like electric field periodicity, and comparing its performance to universal codes.

Contribution

It identifies fundamental trade-offs and limitations of GLQEC, including the requirement for periodic electric fields and its decoherence behavior under multiple error correction rounds.

Findings

GLQEC requires periodic electric fields, constraining lattice QED design.

GLQEC achieves lower error rates in single-round correction but decoheres faster over multiple rounds.

A mixing speed threshold of p_{th}=0.277(2) determines when GLQEC becomes less effective than no correction.

Abstract

Gauss's law-based quantum error correction (GLQEC) offers a promising approach to reducing qubit overhead in lattice gauge theory simulations by leveraging built-in symmetries. For applications of GLQEC to 1+1D lattice quantum electrodynamics (QED), we identify two significant trade-offs. First, we prove via dimension-counting arguments that GLQEC requires periodic electric fields, thereby constraining the design space for lattice QED simulations. Second, we numerically compare GLQEC with a universal quantum error correction (UQEC) code, specifically the $d=3$ bitflip repetition code, and find that while GLQEC can achieve lower logical error rates in single-round error correction, it exhibits faster decoherence to the steady-state mixed ensemble under multiple rounds. The mixing speed penalty is manifest in observables of interest for both memory experiments and Hamiltonian evolution. We identify a mixing speed threshold, $p_{th}=0.277(2)$, above which using GLQEC exhibits even faster decoherence than without error correction. Our results highlight fundamental limitations of symmetry-based error correction schemes and inform corresponding constraints on formulations of lattice gauge theories compatible with error-robust quantum simulation techniques.