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

TL;DR

This paper introduces a reinforcement learning-enhanced decoding method for quantum stabilizer codes derived from algebraic curves, demonstrating significant performance improvements over traditional greedy decoding in simulations.

Contribution

It presents a novel RL-on-Greedy decoding algorithm that combines classical syndrome decoding with deep reinforcement learning for quantum codes from algebraic curves.

Findings

RL-on-Greedy reduces logical failure rates significantly.

The method applies to codes from separated polynomial curves.

Simulation results show near-optimal decoding performance.

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.