利用强化学习发现高效轻量级量子纠错码

Discovering highly efficient low-weight quantum error-correcting codes with reinforcement learning

February 20, 2025

作者: Austin Yubo He, Zi-Wen Liu

cs.AI

摘要

实现可扩展的容错量子计算，预计将依赖于量子纠错码。在追求更高效的量子容错过程中，一个关键的编码参数是用于提取错误信息以进行纠错的测量权重：由于更高的测量权重需要更高的实现成本并引入更多错误，因此在编码设计中优化测量权重至关重要。这推动了人们对量子低密度奇偶校验（qLDPC）码日益增长的兴趣，其研究主要集中在渐近（大码限）特性上。在本研究中，我们引入了一种基于强化学习（RL）的通用且计算高效的稳定子码权重降低方法，该方法生成了新的低权重码，在实际相关参数范围内显著超越了现有技术水平，并大幅扩展了之前可触及的小距离范围。例如，对于权重为6的编码，我们的方法相比现有结果在物理量子比特开销上节省了1到2个数量级，并将开销带入了近未来实验的可行范围。我们还利用RL框架研究了编码参数之间的相互作用，为实际可行的编码策略的潜在效率和能力提供了新的见解。总体而言，我们的结果表明，RL如何有效推进量子码发现这一关键而具挑战性的问题，从而加速容错量子技术的实际实现进程。

English

The realization of scalable fault-tolerant quantum computing is expected to hinge on quantum error-correcting codes. In the quest for more efficient quantum fault tolerance, a critical code parameter is the weight of measurements that extract information about errors to enable error correction: as higher measurement weights require higher implementation costs and introduce more errors, it is important in code design to optimize measurement weight. This underlies the surging interest in quantum low-density parity-check (qLDPC) codes, the study of which has primarily focused on the asymptotic (large-code-limit) properties. In this work, we introduce a versatile and computationally efficient approach to stabilizer code weight reduction based on reinforcement learning (RL), which produces new low-weight codes that substantially outperform the state of the art in practically relevant parameter regimes, extending significantly beyond previously accessible small distances. For example, our approach demonstrates savings in physical qubit overhead compared to existing results by 1 to 2 orders of magnitude for weight 6 codes and brings the overhead into a feasible range for near-future experiments. We also investigate the interplay between code parameters using our RL framework, offering new insights into the potential efficiency and power of practically viable coding strategies. Overall, our results demonstrate how RL can effectively advance the crucial yet challenging problem of quantum code discovery and thereby facilitate a faster path to the practical implementation of fault-tolerant quantum technologies.