Adaptive-depth randomized measurement for fermionic observables

Kaiming Bian

doi:doi:10.1088/2058-9565/adeeb9

2025-07-21

PRE

Kaiming Bian

Bujiao Wu *

DOI：doi:10.1088/2058-9565/adeeb9

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摘要

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对费米子可观测量进行准确估计对于推动量子物理和化学的发展至关重要。费米子经典影射（FCS）方法提供了一种高效框架，用于估计这些可观测量，而无需将k-局域费米子可观测量变换为泡利基。然而，FCS中的随机匹配门电路需要具有砖石结构线性深度的电路，这对计算资源有限的近期量子设备构成了显著挑战。为解决此限制，我们引入了一种自适应深度费米子经典影射（ADFCS）协议，旨在减少电路深度同时保持样本复杂度。通过理论分析和数值拟合，我们确立：当局域性k为常数时，近似费米子可观测量H所需的深度上限为（其中dint为H的相互作用距离，n为量子比特数）。我们通过数值实验展示了ADFCS协议的有效性，结果表明其与传统FCS方法具有相似的精度，同时显著减少了所需的量子资源。此外，我们将ADFCS应用于计算基塔耶链哈密顿量的期望值，进一步验证了其在实际场景中的性能。我们的研究结果表明，当局域性k为常数时，ADFCS能够实现更高效的量子模拟，在减少电路深度的同时保持样本复杂度，并为近期量子设备提供了一种可行的解决方案。

Keyword:

fermionic classical shadow

adaptive-depth

quantum simulation

k-local observables

near-term quantum devices

期刊

Quantum Science and Technology

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