Non-Abelian Quantum Low-Density Parity Check Codes and Non-Clifford Operations from Gauging Logical Gates via Measurements

• URL: http://arxiv.org/abs/2602.12228v1
• Date: Thu, 12 Feb 2026 18:05:23 GMT
• Title: Non-Abelian Quantum Low-Density Parity Check Codes and Non-Clifford Operations from Gauging Logical Gates via Measurements
• Authors: Maine Christos, Chiu Fan Bowen Lo, Vedika Khemani, Rahul Sahay,
• Abstract summary: We introduce constructions for non-Abelian qLDPC codes obtained by gauging Clifford gates.<n>Our constructions offer a protocol for performing non-Clifford operations on any qLDPC code.
• Score: 0.00269220799495636
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we introduce constructions for non-Abelian qLDPC codes obtained by gauging transversal Clifford gates using measurement and feedback. In particular, we identify two qualitatively different approaches to gauging qLDPC codes to obtain their non-Abelian counterparts. The first approach applies to codes that exhibit a generalized form of Poincaré duality and leads to a qLDPC non-Abelian Clifford stabilizer code, whose stabilizers are reminiscent of the action of a Type-III twisted quantum double. Our second approach applies to general qLDPC codes, and uses a graph of ancilla qubits which may be tailored to properties of the input codes to gauge a single transversal gate. For both constructions, the resulting gauged codes are shown to have properties analogous to 2D non-Abelian topological order -- e.g. the analog of a single anyon on a torus. We conclude by demonstrating that our gauging procedures enable magic state preparation via the measurement of logical Clifford gates. Consequently, our gauging constructions offer a protocol for performing non-Clifford operations on any qLDPC code.

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