随机监测量子纠错码中的同调阈值
Homological Thresholds in Randomly Monitored Quantum Error-Correcting Codes
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中文总结 AI 辅助
本研究揭示随机监测下稳定子量子纠错码的阈值行为分为几何与同调两类渗流转变，通过大规模模拟确定临界指数，并扩展至多种码型，为解码提供指导。
中文摘要 AI 辅助
随机投影测量是模拟监测、推断和解码高度纠缠态（如量子纠错码）相互关联现象的有效工具。同时，对这种监测动力学的研究为临界现象开辟了新的领域，重新激发了无序统计力学中长期存在的问题，包括渗流、随机键模型和西森里物理。在此，我们研究了稳定子量子纠错码在单轮独立采样的单量子比特泡利测量下的鲁棒性，并证明其阈值行为分为两大类——几何渗流转变和同调渗流转变，其中环面码和色码分别是每一类的主要示例。通过分析这些码的逻辑支持准则，并利用对超过一百万量子比特的大规模系统进行优化的稳定子模拟，提供各自临界指数的数值估计，我们确立了这两种阈值理论的不同特征。我们的框架扩展到非CSS码、子系统码、高维码和Floquet稳定子码，并使我们能够确定它们各自的阈值相图。我们举例说明了后者如何为计算上更困难的可调学习和最大似然解码问题提供定量和定性指导。作为我们框架的一个实际应用，我们讨论了gross码的鲁棒性。
英文摘要
Random projective measurements are an effective tool to model the interlinked phenomenology of monitoring, inferring, and decoding highly entangled states such as quantum error-correcting codes. At the same time, the study of such monitored dynamics has opened a new arena for critical phenomena, renewing longstanding questions in disordered statistical mechanics, including percolation, random-bond models, and Nishimori physics. Here we investigate the robustness of stabilizer quantum error-correcting codes under a single round of independently sampled single-qubit Pauli measurements and demonstrate that their threshold behavior falls into two broad categories - geometric and homological percolation transitions, with the toric code and color code being the principal examples for each class. We establish the distinct character of these two threshold theories by analyzing the logical-support criteria of these codes and by providing numerical estimates of their respective critical exponents obtained from optimized stabilizer simulations of large-scale systems with over one million qubits. Our framework extends to non-CSS, subsystem, higher-dimensional, and Floquet stabilizer codes and allows us to determine their respective threshold phase diagrams. We exemplify how the latter provide quantitative and qualitative guidance for the computationally more demanding problems of tunable learning and maximum-likelihood decoding. As a practical application of our framework, we discuss the robustness of the gross code.
发表机构
- Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）
- Department of Physics, Graduate School of Science, Tohoku University（东北大学理学研究科物理学系）
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