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

• URL: http://arxiv.org/abs/2602.22121v1
• Date: Wed, 25 Feb 2026 17:09:20 GMT
• Title: Trade-offs in Gauss's law error correction for lattice gauge theory quantum simulations
• Authors: Balint Pato, Natalie Klco,
• Abstract summary: 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.<n>We numerically compare GLQEC with a universal quantum error correction 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.<n>Our results highlight fundamental limitations of symmetry-based error correction schemes and inform corresponding constraints on formulations of lattice gauge theories
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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