Unification and Improvement of Quantum Error Mitigation Methods by Generalized Quantum Subspace Expansion*

Numerous quantum error mitigation methods are proposed to make the most of noisy quantum devices that lack the capability of quantum error correction. Probabilistic error cancellation (PEC) and symmetry verification are representative quantum error mitigation methods. PEC can effectively mitigate well-characterized noise by inverting the noise virtually. However, if the characterization or modeling of noise is inaccurate, PEC may mitigate the bias to a limited extent or even increase it. Furthermore, although the symmetry verification mitigates detectable errors, the method is by construction vulnerable to undetectable errors. In this study, we show that generalized quantum subspace expansion (GSE) enables us to apply the PEC without the need for an accurate characterization or modeling of noise and mitigates the bias of the undetectable errors for the symmetry verification. As a demonstration of these techniques, we numerically estimate the ground energy of the transverse-field Ising model. We believe that our proposed methods and results offer practical insights for implementing the existing quantum error mitigation methods.