  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 $\mathrm{U(1)}$ 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.
