Reinforcement Learning Enhanced Greedy Decoding for Quantum Stabilizer Codes over $\mathbb{F}_q$

• URL: http://arxiv.org/abs/2506.03397v1
• Date: Tue, 03 Jun 2025 21:08:36 GMT
• Title: Reinforcement Learning Enhanced Greedy Decoding for Quantum Stabilizer Codes over $\mathbb{F}_q$
• Authors: Vahid Nourozi,
• Abstract summary: We construct new classical Goppa codes and corresponding quantum stabilizer codes from plane curves defined by separateds.<n>Our work thus broadens the class of Goppa- and quantum-stabilizer codes from separated-polynomial curves and delivers a learned decoder with near-optimal performance.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We construct new classical Goppa codes and corresponding quantum stabilizer codes from plane curves defined by separated polynomials. In particular, over $\mathbb{F}_3$ with the Hermitian curve $y^3 + y = x^4$, we obtain a ternary code of length 27, dimension 13, distance 4, which yields a [[27, 13, 4]]$_3$ quantum code. To decode, we introduce an RL-on-Greedy algorithm: first apply a standard greedy syndrome decoder, then use a trained Deep Q-Network to correct any residual syndrome. Simulation under a depolarizing noise model shows that RL-on-Greedy dramatically reduces logical failure compared to greedy alone. Our work thus broadens the class of Goppa- and quantum-stabilizer codes from separated-polynomial curves and delivers a learned decoder with near-optimal performance.

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