逻辑魔力状态的高效基准测试
Su-Un Lee1, Ming Yuan1, Senrui Chen1
1Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA.
Physical review letters
|February 22, 2026
概括
对于量子计算来说,对高保真度魔力状态进行基准测试是具有挑战性的. 使用贝尔测量或多量子比特状态的新方法可以将样本的复杂性从二进制到线性降低,从而实现实际验证.
科学领域:
- 量子信息科学 量子信息科学
- 量子计算是一种量子计算.
- 量子错误纠正方法 量子错误纠正方法
背景情况:
- 高保真度魔力状态对于容错量子计算至关重要,使关键的非克利福德运算成为可能.
- 目前的基准测试方法 (状态断层扫描) 需要不切实际的大样本大小 (比例为1/ε2) 对于高保真状态.
- 量子错误纠正代码经常将操作限制在容错的克利福德门上,使魔力状态的基准测试复杂化.
研究的目的:
- 为了应对高保真度魔力状态的高效基准测试的挑战.
- 开发新的协议,克服传统方法的二次性样本复杂性限制.
- 为了实现最佳的O(1/ε) 样本复杂性,用于魔力状态的基准测试.
主要方法:
- 分析单复制魔力状态基准测试的样本复杂性,证明下限为 Ω(1/ε2).
- 提出两种新的基准测试方案:对两个旋转的魔力状态的钟测量和对旋转的多量子比特魔力状态的单复制方案.
- 利用在拟议方案中与理想魔力状态直角的稳定器状态进行测量.
主要成果:
- 证明任何单复制的基准测试方案都需要为单量子比特魔力状态提供 Ω{\displaystyle Ω}1/ε2 的样本.
- 使用建议的贝尔测量和多量子比特旋转状态协议,实现了最佳的O(1/ε) 样本复杂性.
- 证明了O{1/ε) 样本复杂度对开发的基准测试方案的最佳性.
结论:
- 开发的协议为比较魔力状态的样本复杂性提供了显著的改进.
- 这些方法在现实的噪声模型下是可靠的,数字模拟证实了这一点.
- 这些发现为对容错量子计算所需资源的实际验证铺平了道路.
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