Low-cost error mitigation by symmetry verification

By X. Bonet-Monroig, R. Sagastizabal, M. Singh, T. O’Brien. Physical Review A, 2018

261 citations recorded by the source corpus.

We investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an experiment, and develop a third, zero-cost, post-processing protocol which is equivalent to a variant of the quantum subspace expansion. We develop methods for inserting global and local symmetries into quantum algorithms, and for adjusting natural symmetries of the problem to boost the mitigation of errors produced by different noise channels. We demonstrate these techniques on two- and four-qubit simulations of the hydrogen molecule (using a classical density-matrix simulator), finding up to an order of magnitude reduction of the error in obtaining the ground-state dissociation curve.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/6f8b68026cc119b65c7ed0ca272502704fc47ee4

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Theory of variational quantum simulation (2018, methodology): “As the variational method only uses shallow quantum circuits, error mitigation techniques can be applied to suppress errors [41, 63–70].”
Error mitigation with Clifford quantum-circuit data (2020, background): “Among other approaches are quasi-probabilistic error mitigation [45] and numerous application specific approaches leveraging symmetries and/or post-selection techniques to mitigate errors [4, 7, 32, 38].”
Quantum error mitigation (2022, methodology): “The broad class of schemes that directly or indirectly measure Tr[ Oρ sym ] are known collectively as symmetry verification (Bonet-Monroig et al. , 2018; McArdle et al. , 2019).”
Variational Quantum Computation of Excited States (2018, methodology): “[3, 22, 34], an error-mitigating post-processing procedure was introduced that uses the operators Ĉi (defined in Appendix E) to detect and discard all measurements that violate a required symmetry for energy expectation circuits in VQE-type algorithms.”
Variational quantum algorithms (2020, methodology): “One can also take a post-processing approach using the information of the symmetry with a larger sample number [215].”