通过经典阴影和对称性实现群论误差缓解

IF 6.6 1区 物理与天体物理 Q1 PHYSICS, APPLIED
Andrew Zhao, Akimasa Miyake
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引用次数: 0

摘要

估计期望值是量子算法中的一个关键子程序。近期的实现面临两大挑战:学习大量观测值所需的样本数量有限,以及在没有量子纠错的设备中误差的积累。为了同时应对这些挑战,我们开发了一种称为对称性调整经典阴影的量子纠错策略,根据对称性如何被器件误差破坏来调整经典阴影层析成像。作为一个具体例子,我们强调了全局 U(1) 对称性,它在费米子中表现为粒子数,在自旋中表现为总磁化,并说明了它们与各自经典阴影协议的群论统一。我们建立了符合最小假设的读出误差下的严格采样边界,并利用从现有量子处理器中得出的更全面的门级误差模型进行了数值实验。我们的结果揭示了对称调整经典阴影是一种低成本策略,可以在对称性无处不在的情况下减轻来自噪声量子实验的误差。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Group-theoretic error mitigation enabled by classical shadows and symmetries

Group-theoretic error mitigation enabled by classical shadows and symmetries

Estimating expectation values is a key subroutine in quantum algorithms. Near-term implementations face two major challenges: a limited number of samples required to learn a large collection of observables, and the accumulation of errors in devices without quantum error correction. To address these challenges simultaneously, we develop a quantum error-mitigation strategy called symmetry-adjusted classical shadows, by adjusting classical-shadow tomography according to how symmetries are corrupted by device errors. As a concrete example, we highlight global U(1) symmetry, which manifests in fermions as particle number and in spins as total magnetization, and illustrate their group-theoretic unification with respective classical-shadow protocols. We establish rigorous sampling bounds under readout errors obeying minimal assumptions, and perform numerical experiments with a more comprehensive model of gate-level errors derived from existing quantum processors. Our results reveal symmetry-adjusted classical shadows as a low-cost strategy to mitigate errors from noisy quantum experiments in the ubiquitous presence of symmetry.

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来源期刊
npj Quantum Information
npj Quantum Information Computer Science-Computer Science (miscellaneous)
CiteScore
13.70
自引率
3.90%
发文量
130
审稿时长
29 weeks
期刊介绍: The scope of npj Quantum Information spans across all relevant disciplines, fields, approaches and levels and so considers outstanding work ranging from fundamental research to applications and technologies.
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