Noisy Probabilistic Error Cancellation and Generalized Physical Implementability

Abstract: Quantum decoherent noises have significantly influenced the performance of practical quantum processors. Probabilistic error cancellation quantum error mitigation method quasiprobabilistically simulates the noise inverse operations, which are not physical channels, to cancel the noises. Physical implementability is the minimal cost to simulate a non-physical quantum operation with physical channels by the quasiprobabilistic decomposition. However, in practical, this cancellation may also be influenced by noises, and the implementable channels are not all of the physical channels, so the physical implementability is not sufficient to completely depict the practical situation of the probabilistic error cancellation method. Therefore, we generalize the physical implementability to an arbitrary convex set of free quantum resources and discuss several of its properties. We demonstrate the way to optimally cancel the error channel with the noisy Pauli basis. In addition, we also discuss the several properties relevant to this generalization. We expect that its properties and structures will be investigated comprehensively, and it will have more applications in the field of quantum information processing.