Group-theoretic error mitigation enabled by classical shadows and symmetries

TL;DR

This paper introduces symmetry-adjusted classical shadows, a novel quantum error mitigation technique leveraging symmetries to improve expectation value estimation in noisy quantum devices.

Contribution

It develops a new error mitigation method that incorporates symmetries into classical-shadow tomography, with rigorous bounds and practical demonstrations.

Findings

Effective error mitigation for symmetry-related observables

Rigorous sampling bounds under readout errors

Numerical validation on realistic quantum error models

Abstract

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.