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- Title
Group-theoretic error mitigation enabled by classical shadows and symmetries.
- Authors
Zhao, Andrew; Miyake, Akimasa
- 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.
- Subjects
PARTICLE spin; SYMMETRY; FERMIONS; EXPECTATION-maximization algorithms
- Publication
NPJ Quantum Information, 2024, Vol 10, Issue 1, p1
- ISSN
2056-6387
- Publication type
Article
- DOI
10.1038/s41534-024-00854-5