Error Correction in Lattice Quantum Electrodynamics with Quantum Reference Frames

TL;DR

This paper explores how gauge symmetry in lattice quantum electrodynamics can be understood as a quantum error-correcting code, using quantum reference frames to identify and correct errors, thus revealing a deeper information-theoretic role.

Contribution

It constructs explicit QECC structures in lattice QED using group-theoretical methods and quantum reference frames, extending the understanding of gauge theories as error-correcting codes.

Findings

Explicit recovery operations for Abelian gauge groups are constructed.

Two QECC structures are identified: one in the pure-gauge sector and one with fermions.

Quantum reference frames resolve degeneracies in error syndromes, enabling error correction.

Abstract

Is gauge symmetry merely a redundancy in our description, or does it carry a deeper information-theoretic significance? Quantum error-correcting codes (QECCs) show that redundancy can serve as a resource for protecting information against noise. In this work, we ask whether gauge theories can be understood in similar terms, and make this idea concrete in lattice quantum electrodynamics (QED), building on and extending earlier works that established a bridge between gauge systems, stabilizer codes, and quantum reference frames (QRFs). For Abelian gauge groups, we show that explicit recovery operations can be constructed using group-theoretical methods for error sets determined by both ideal and non-ideal QRFs. Applied to lattice QED, this yields two QECC structures: one in the pure-gauge sector and one including fermions. We construct a gauge-field QRF based on spanning trees of the lattice and a fermionic field QRF from the matter field, thereby making explicit how physical information is encoded. While the syndromes of gauge-violating errors associated with constraint measurements are generically degenerate, QRFs resolve this degeneracy and single out families of correctable errors. This establishes lattice QED as a QECC beyond the stabilizer setting and shows concretely how gauge symmetry provides an encoding structure that supports error correction.