Fig. 3: Error-mitigation protocols.
Our framework encompasses all commonly used error-mitigation protocols, a sample of which we outline here. A Probabilistic error cancellation3 assumes we can only act a single coherent state each round, where it seeks to undo a given noise map \({{{\mathcal{E}}}}\) by applying a suitable stochastic operation \({{{\mathcal{B}}}}\). Thus it corresponds to the case of Q = K = 1. B Rth order noise extrapolation assumes3,4 the capacity to synthesize R + 1 NISQ devices whose outputs represent distortions of ψ at various noise strengths. It then uses individual measurements of an observable A on these distorted states to estimate the observable expectation value on the zero-noise limit. Thus it is an example where Q = 1 and K = R + 1. C Meanwhile, R-copy virtual distillation14,15 involves running an available NISQ device R times to synthesize R copies of a distorted state \({{{\mathcal{E}}}}(\psi )\). Coherent interaction \({{{\mathcal{D}}}}\) over these copies followed by a suitable measurement MA then enables improved estimation of 〈A〉. Thus it is an example where K = 1 and Q = R. In the main text and Methods, we provide a detailed account of each protocol and how it fits within our framework.
