使用Clifford稳定子对含噪逻辑魔态进行精确高效模拟
Exact efficient simulation of noisy logical magic states using Clifford stabilizers
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中文总结 AI 辅助
本文提出Clifford稳定子模拟算法，通过将含噪非Clifford电路映射为等价Clifford电路，实现逻辑魔态制备协议的精确高效经典模拟，并成功模拟至故障距离7，为FTQC基准测试提供新途径。
中文摘要 AI 辅助
高保真逻辑魔态的制备是通用容错量子计算（FTQC）的关键子程序。预测FTQC的性能以及开发改进协议，依赖于在存在噪声的情况下经典模拟逻辑魔态制备的数值方法。对于具有电路级Pauli错误的Pauli稳定子码，Clifford逻辑可以使用Pauli稳定子形式体系进行高效模拟，但制备逻辑魔态所需的非Clifford操作使得通用模拟效率低下。我们引入了Clifford稳定子模拟，这是一种基于更新Clifford稳定子群的精确高效算法，用于模拟在电路级Pauli错误下，制备用于实现Clifford层级第三层中非Clifford门的一类广泛逻辑魔态的含噪制备协议。Clifford稳定子模拟适用于此类逻辑魔态制备协议中常见的一系列操作，包括Pauli稳定子测量、逻辑Clifford测量和横向非Clifford门。我们的Clifford稳定子模拟算法将具有采样电路级Pauli错误的非Clifford电路映射到精确再现其测量结果分布的Clifford电路，实现了与相关协议参数成多项式关系的时间和空间复杂度。我们通过Clifford稳定子模拟，对故障距离高达7的魔态培养进行了精确模拟。我们的方法为对有用FTQC所需的大规模逻辑魔态制备协议进行精确基准测试提供了途径。
英文摘要
The preparation of high-fidelity logical magic states is a crucial subroutine for universal fault-tolerant quantum computation (FTQC). Predicting the performance of FTQC and developing improved protocols rely on numerical methods to classically simulate logical magic state preparation in the presence of noise. Clifford logic on Pauli-stabilizer codes with circuit-level Pauli errors can be efficiently simulated using Pauli-stabilizer formalism, but the non-Clifford operations required to prepare logical magic states render generic simulation inefficient. We introduce Clifford-stabilizer simulation, an exact and efficient algorithm based on updating a Clifford-stabilizer group to simulate noisy preparation protocols for a broad class of logical magic states used to implement non-Clifford gates in the third level of the Clifford hierarchy under circuit-level Pauli errors. Clifford-stabilizer simulation applies to a range of operations that commonly appear in preparation protocols for such logical magic states, including Pauli-stabilizer measurements, logical Clifford measurements, and transversal non-Clifford gates. Our algorithm for Clifford-stabilizer simulation maps a non-Clifford circuit with sampled circuit-level Pauli errors to a Clifford circuit that exactly reproduces its measurement outcome distribution, achieving time and space complexities polynomial in relevant protocol parameters. We perform exact simulation of magic state cultivation up to fault distance 7 by Clifford-stabilizer simulation. Our method provides a route to perform exact benchmarking of large-scale logical magic state preparation protocols required for useful FTQC.
发表机构
- Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科）
- School of Physics, The University of Sydney（悉尼大学物理学院）
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