发表机构
QuEra Computing Inc.; Joint Center for Quantum Information and Computer Science, University of Maryland; Simons Institute for the Theory of Computing, University of California at Berkeley; Institute for Theoretical Physics, ETH Zürich; Department of Physics, Harvard University（QuEra 计算公司; 马里兰大学量子信息与计算机科学联合中心; 加州大学伯克利分校西蒙斯计算理论研究所; 苏黎世联邦理工学院理论物理研究所; 哈佛大学物理学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种高效的经典模拟方法，用于基准测试含非克利福德门的容错电路，通过采样综合征统计量估计逻辑保真度，并应用于优化高比率魔法态蒸馏工厂。
AI 中文摘要
非克利福德门对于在 Gottesman-Knill 定理下避免经典可模拟性至关重要。因此，包含非克利福德门的纠错电路将是实现实用容错量子算法的关键要素。然而，由于模拟这些电路的经典难度，准确理解此类电路的容错性能面临挑战。我们避免模拟逻辑测量，并为基准测试由 X、CNOT 和 Clifford 层级中的对角门组成的电路（包括具有前馈的态和门隐形传态工具）开发了精确且高效的经典方法。对于包含第三层对角门的电路，我们的基准测试算法高效地采样综合征统计量，并估计输出逻辑保真度和某些 Clifford 可观测量的期望值，包括所有 Pauli 可观测量。综合征期望值的评估也扩展到包含第四层对角门的电路。我们的算法在物理量子比特数 n 和电路深度 T 上呈多项式缩放，与逻辑量子比特数无关。基准测试应用包括 IQP 采样和魔法态制备/培育。我们通过使用这些算法优化基于三个 [[27,3,3]] 三轮车码副本的高比率魔法态蒸馏工厂，展示了我们模拟算法的实际效用。
英文摘要
Non-Clifford gates are essential for avoiding classical simulability under the Gottesman-Knill theorem. An error-corrected circuit with non-Clifford gates will therefore be an important element for realizing useful fault-tolerant quantum algorithms. However, accurately understanding the fault-tolerant performance of such circuits faces challenges due to the classical hardness of simulating these circuits. We avoid simulating logical measurements and develop exact and efficient classical methods for benchmarking circuits composed of X, CNOT, and diagonal gates in the Clifford hierarchy, including state and gate teleportation gadgets with feedforward. For circuits with third-level diagonal gates, our benchmarking algorithm efficiently samples syndrome statistics and estimates the output logical fidelity and expectation values of certain Clifford observables, including all Pauli observables. The evaluation of syndrome expectation values also extends to circuits with fourth-level diagonal gates. Our algorithm scales polynomially in the number of physical qubits n and circuit depth T, independent of the number of logical qubits. The benchmarking applications include IQP sampling and magic state preparation/cultivation. We demonstrate the practical utility of our simulation algorithms by using them to optimize high-rate magic state distillation factories based on three copies of a [[27,3,3]] tricycle code.
Comments28 pages, 6 figures
