Title: Quantum magnetometry using discrete-time quantum walk

Abstract: Quantum magnetometry uses quantum resources to measure magnetic fields with precision and accuracy that cannot be achieved by its classical counterparts. In this paper, we propose a scheme for quantum magnetometry using discrete-time quantum walk (DTQW) where multi-path interference plays a central role. The dynamics of a spin-half particle implementing DTQW on a one-dimensional lattice gets affected by magnetic fields, and the controlled dynamics of DTQW help in estimating the fields' strength. To gauge the effects of the field, we study the variance of the particle's position probability distribution (PD) and use it to determine the direction of the magnetic field maximally affecting the quantum walk. We then employ statistical tools like quantum Fisher information (QFI) and Fisher information (FI) of the particle's position and spin measurements to assess the system's sensitivity to the magnetic fields. We find that one can use the position and spin measurements to estimate the strengths of the magnetic fields. Calculations for an electron implementing quantum walk of fifty time steps show that the estimate had a root-mean-square error of the order of 0.1 picoTesla. Moreover, the sensitivity of our system can be tuned to measure any desired magnetic field. Our results indicate that the system can be used as a tool for optimal quantum magnetometry.