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.

估计期望值是量子算法中的一个关键子程序。近期的实现面临两个主要挑战：学习大量可观测值所需的样本数量有限，以及没有量子纠错的设备中的错误累积。为了同时应对这些挑战，我们开发了一种称为对称调整经典阴影的量子误差缓解策略，通过根据设备误差如何破坏对称性来调整经典阴影断层扫描。作为一个具体的例子，我们强调全局 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强度，并用各自的经典阴影协议说明它们的群论统一。我们在遵守最小假设的读出误差下建立了严格的采样范围，并使用从现有量子处理器导出的更全面的门级误差模型进行数值实验。我们的结果表明，对称性调整的经典阴影是一种低成本策略，可以减少对称性无处不在的嘈杂量子实验中产生的误差。