Error-mitigated quantum metrology

Quantum metrology with entangled resources has the potential to achieve the sensitivity that is called the Heisenberg limit. Since the sensitivity is reduced by environmental noise, many theoretical efforts have been made to recover the sensitivity under the effect of decoherence. Conventionally, most of the theoretical protocols have focused only on statistical errors under the assumption that the noise model can be fully characterized. However, contrary to theoretical interests, noise fluctuates in time, for example, a fluctuation of the coherence time has been observed; accordingly, noise characterization is intractable, and then leads to systematic errors. Systematic errors usually come from a difference between a theoretical model and the actual one, and remain almost unexplored theoretically for the quantum metrology.

Here,  we propose an error-mitigated quantum metrology incorporating quantum error mitigation (QEM) to exponentially mitigate systematic errors, thus improving the sensitivity even under fluctuating noise. We have theoretically revealed that our error-mitigated quantum metrology inspired by the purification-based QEM can filter out fluctuating noise which differs in each experimental run. Then we apply our method to suppress bias-inducing Markovian and time-inhomogeneous noise to demonstrate the restoration of the scaling of sensitivity with respect to the number of qubits. In particular, for the latter case, we can observe the superclassical scaling by using our method.