Framework of Generalized Quantum Subspace Expansion Method*

Undoubtedly it is crucial to control the effect of noise to achieve computational advantage using erroneous quantum computers. Since the rapidly growing quantum resources are still years or decades away from full fault tolerance, the near-term challenge would be to develop practical hardware-friendly quantum error mitigation (QEM) techniques. In this work, we propose a generalization of the quantum subspace expansion method which is capable of mitigating all stochastic, coherent, and algorithmic errors in quantum computers. We show that, without relying on any information of noise, the error in the energy spectra of a given Hamiltonian can be mitigated efficiently. The performance of our method is investigated under two highly practical setups, in which the quantum subspaces are mainly spanned by powers of a noisy state ρ^m and a set of error-boosted states, respectively.  In both situations, we provide numerical demonstrations that we can suppress error by orders of magnitude, and also that our protocol inherits the advantages of previous error-agnostic QEM techniques.