发表机构
University of Saskatchewan; Centre for Quantum Topology and Its Applications (quanTA); Department of Mathematics and Statistics（萨斯喀彻温大学; 量子拓扑及其应用中心; 数学与统计系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出几何优化的双曲表面码，通过优化周期标识提升效率，引入拓扑感知算法解决路由问题，经模拟验证其可作为高效大规模量子纠错码用于模块化容错量子架构。
AI 中文摘要
量子容错是充分发挥量子计算机全部潜力的前提条件。然而，实现容错仍是一项重大挑战，因为它需要在多个相互关联的理论和实验参数之间进行权衡优化，这些参数包括编码率、码距、奇偶校验权重、码平面性和路由。表面码因其简单的几何结构、成熟的解码方法、局域性和实验可实现性，仍是容错的有力候选方案。在本研究中，我们提出了有限族双曲表面码，其利用了具有有界局域几何的表面码可达到的最优效率标度 $kd^2/n = C (\text{log}k)^2$。我们表明，优化周期标识可使码距翻倍，从而在固定量子比特数、编码率和奇偶校验权重的情况下，将码的效率提高4倍。我们还通过引入一种拓扑感知算法解决了双曲表面码的路由问题，该算法将双曲码划分为有界平面模块，同时降低了对长程通信的需求。电路级蒙特卡罗模拟得出了模块化和整体布局的有限尺寸阈值估计，表明将长程门错误概率提高2倍会轻微降低，但不会消除估计的纠错阈值。这些结果共同为双曲表面码作为未来容错架构的结构化且高效的大规模量子纠错码提供了有力支持。
英文摘要
Quantum fault tolerance is a prerequisite to harness the full potential of quantum computers. However, achieving fault tolerance remains a major challenge since it requires optimizing tradeoffs between several intertwined theoretical and experimental parameters, including the encoding rate, code distance, parity-check weights, code planarity, and routing. Surface codes remain strong candidates for fault tolerance due to their simple geometric structure, established decoding methods, locality, and experimental attainability. In this work, we present finite families of hyperbolic surface codes that leverage the optimal efficiency scaling $kd^2/n = C (\log{k})^2$ attainable by surface codes with bounded local geometry. We show that optimizing the periodic identifications can double the code distance and thereby increase the code's efficiency by a factor of four, at fixed qubit count, encoding rate, and parity-check weight. We also address the routing problem of hyperbolic surface codes by introducing a topology-aware algorithm that partitions a hyperbolic code into bounded planar modules while reducing long-range communications demand. Circuit-level Monte Carlo simulations yield finite-size threshold estimates for both modular and monolithic layouts, showing that tripling the long-range gate error probability mildly lowers, but does not eliminate, the estimated error-correction thresholds. Together, these results strengthen the case for hyperbolic surface codes as structured and highly efficient large-scale quantum error correction codes for future fault-tolerant architectures.
Comments14 pages, 6 figures, 4 tables
