Group-theoretic error mitigation enabled by classical shadows and symmetries

• URL: http://arxiv.org/abs/2310.03071v3
• Date: Sat, 15 Jun 2024 00:28:25 GMT
• Title: Group-theoretic error mitigation enabled by classical shadows and symmetries
• Authors: Andrew Zhao, Akimasa Miyake,
• Abstract summary: 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. We develop a quantum error-mitigation strategy called symmetry-adjusted classical shadows'' 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.
• Score: 2.378735224874938
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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