探测矩阵乘积态下的纠错缓解阈值
Probing the Error-Mitigation Threshold with Matrix Product States
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- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学联合量子研究所与联合量子信息与计算科学中心）
- National Institute of Standards and Technology（美国国家标准与技术研究院）
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中文总结 AI 辅助
本文提出固定键维矩阵乘积态方法，用于探测量子纠错缓解阈值，在大型二维电路中恢复一维阈值缺失并解析架构依赖的有限深度阈值。
中文摘要 AI 辅助
量子纠错缓解依赖于精确的噪声表征，但实际噪声与表征噪声之间的失配可能被放大，并驱动成功与失败缓解之间的尖锐阈值。在随机电路中，该阈值映射到随机场伊辛相变，但先前的精确数值计算仅限于一维和全连接的小型系统，使得二维架构的显式研究悬而未决。我们开发了一种固定键维矩阵乘积态方法，用于复制转移动力学，将阈值计算扩展到精确传播之外，同时保留相变的有限尺寸特征。在超出先前精确研究的系统尺寸下，我们恢复了在一维淬火无序中预测的阈值缺失，获得了更尖锐的退火全连接临界点，并解析了二维方形和重六角电路中依赖架构的有限深度阈值。这些结果确立了复制张量网络动力学作为探测大型和高维噪声电路中纠错缓解阈值的实用工具。
英文摘要
Quantum error mitigation relies on accurate noise characterization, but mismatches between the actual and characterized noise can be amplified and drive a sharp threshold between successful and failed mitigation. In random circuits, this threshold maps onto a random-field Ising transition, but previous exact numerics were limited to small one-dimensional and all-to-all systems, leaving explicit two-dimensional architectures unresolved. We develop a fixed-bond-dimension matrix-product-state method for the replicated transfer dynamics that extends threshold calculations beyond exact propagation while retaining the finite-size signatures of the transition. At system sizes beyond previous exact studies, we recover the predicted absence of a threshold for quenched disorder in 1D, obtain a sharper annealed all-to-all critical point, and resolve architecture-dependent finite-depth thresholds in 2D square and heavy-hex circuits. These results establish replicated tensor-network dynamics as a practical tool for probing error-mitigation thresholds in large and higher-dimensional noisy circuits.
