Mitigating Markovian Noise in DC Magnetometry via Zero-Noise Extrapolation

Quantum sensors seek to leverage the sensitivity of quantum systems to their environment as a resource to achieve advantages over classical sensors. However, the viability of quantum sensing is challenged in practical settings where noise can lead to undesired evolution and limitations on sensitivity. Within the field of quantum computation, many methods have been developed to address errors induced by noise. Zero-noise extrapolation (ZNE) is one such approach commonly utilized in currently available quantum processors to reduce the effect of noise during the estimation of expectation values. ZNE involves artificially amplifying noise in a controlled way and using measurement outcomes to extrapolate to the zero-noise limit. While ZNE has been extensively studied in quantum computation, it has not been considered in the domain of quantum sensing. In this work, we adapt ZNE to the sensing problem and investigate its effectiveness in mitigating noise in DC magnetometry. We focus on Markovian noise environments and develop unitary folding protocols for the estimation of magnetic field parameters. We demonstrate that ZNE can be used to improve sensing accuracy relative to the standard Ramsey protocol.