论文标题
通过量子近似优化解码综合征
Syndrome decoding by quantum approximate optimization
论文作者
论文摘要
已知综合征解码问题是NP完整的。解码器的目的是找到一个低重量的误差，该误差与从奇偶校验矩阵获得的给定综合征相对应。我们使用量子近似优化算法（QAOA）来解决综合征解码问题，并基于发电机和检查矩阵的经典和量子代码优雅设计的奖励汉密尔顿人。我们评估了[7,4,3]锤码的基于级别4的QAOA解码，以及基于4级生成器的QAOA解码[[5,1,3]]量子代码。值得注意的是，模拟结果表明，解码性能与最大似然解码的性能相匹配。此外，我们通过在组合优化问题上引入其他冗余条款来探索增强QAOA的可能性，同时使量子数不变的数量保持不变。最后，我们研究了简并量子代码的QAOA解码。通常，常规解码器旨在找到与给定综合症相匹配的最小重量的独特误差。但是，我们的观察结果表明，QAOA具有识别可比权重的退化错误的有趣能力，提供了与给定综合征与可比概率相匹配的多种潜在解决方案。通过模拟基于发电机的QAOA解码的[[9,1,3]] Shor代码的特定错误综合症的模拟进行了说明。
The syndrome decoding problem is known to be NP-complete. The goal of the decoder is to find an error of low weight that corresponds to a given syndrome obtained from a parity-check matrix. We use the quantum approximate optimization algorithm (QAOA) to address the syndrome decoding problem with elegantly-designed reward Hamiltonians based on both generator and check matrices for classical and quantum codes. We evaluate the level-4 check-based QAOA decoding of the [7,4,3] Hamming code, as well as the level-4 generator-based QAOA decoding of the [[5,1,3]] quantum code. Remarkably, the simulation results demonstrate that the decoding performances match those of the maximum likelihood decoding. Moreover, we explore the possibility of enhancing QAOA by introducing additional redundant clauses to a combinatorial optimization problem while keeping the number of qubits unchanged. Finally, we study QAOA decoding of degenerate quantum codes. Typically, conventional decoders aim to find a unique error of minimum weight that matches a given syndrome. However, our observations reveal that QAOA has the intriguing ability to identify degenerate errors of comparable weight, providing multiple potential solutions that match the given syndrome with comparable probabilities. This is illustrated through simulations of the generator-based QAOA decoding of the [[9,1,3]] Shor code on specific error syndromes.
