Comment on "Recovering noise-free quantum observables"

Zero-noise extrapolation (ZNE) stands as the most widespread quantum error mitigation technique used in 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 no tunable global noise source [M. Otten et al., Phys. Rev. A 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 nonidentically distributed noise model. The authors proposed a hypersurface method for mitigating such noise, which is technically correct in the sense that if the required samples are obtained, the observable can be mitigated. However, the proposed method presents an excessive experiment repetition overhead, making it impractical, at least from the perspective of quantum computing. Specifically, we discuss that in order to perform a simple mitigation task to multinomial order 3 considering 100 qubits, there, 2.5 years or over a million quantum processors running in parallel would be required. In this Comment, we show that the traditional extrapolation techniques can be applied for such a nonidentically distributed noise setting consisting of many different noise sources, implying that the measurement overhead is practical. In fact, we discuss that the previous mitigation task can be resolved in the order of minutes using a single quantum processor by means of standard ZNE. To do so, we clarify what it is meant by a tunable global noise source in the context of ZNE, a concept that we consider important to be clarified for a correct understanding of how and why these methods work.