Comment on "Recovering noise-free quantum observables"

Abstract

Zero-noise extrapolation (ZNE) stands as the most widespread quantum error mitigation technique in order to aim the recovery of noise-free expectation values of observables of interest by means of Noisy Intermediate-Scale Quantum (NISQ) machines. Recently, Otten and Gray proposed a multidimensional generalization of polynomial ZNE for systems where there is not a tunable global noise source [Phys. Rev. A \textbf{99,} 012338 (2019)]. Specifically, the authors refer to multiqubit systems where each of the qubits experiences several noise processes with different rates, i.e. a non-identically distributed noise model. The authors proposed a hypersurface method for mitigating such noise, which is technically correct. While effective, the proposed method presents an unbearable experiment repetition overhead, making it impractical, at least from the perspective of quantum computing. In this comment, we show that the traditional extrapolation techniques can be applied for such non-identically distributed noise setting consisted of many different noise sources, implying that the measurement overhead is reduced considerably. For doing so, we clarify what it is meant by a tunable global noise source in the context of ZNE, concept that we consider important to be clarified for a correct understanding about how and why these methods work.