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Group-theoretic error mitigation enabled by classical shadows and symmetries
Physicsnpj Quantum Information

Group-theoretic error mitigation enabled by classical shadows and symmetries

A. Zhao and A. Miyake

Discover the revolutionary approach from Andrew Zhao and Akimasa Miyake that tackles the challenges of estimating expectation values in quantum algorithms. Their innovative strategy, symmetry-adjusted classical shadows, mitigates errors in devices even in the absence of quantum error correction, making it a low-cost solution for robust quantum computing.... show more
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 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.
Publisher
npj Quantum Information
Published On
Jun 08, 2024
Authors
Andrew Zhao, Akimasa Miyake
Tags
quantum algorithmserror mitigationclassical shadowssymmetrysampling boundsreadout errorsgate-level error model
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