We propose a quantum fitting scheme to estimate the magnetic field gradient with N-atom spins preparing in W state, which attains the Heisenberg-scaling accuracy. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cram\'{e}r-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. In single parameter estimation with assumption that the magnetic field is strictly linear, two optimal measurements can achieve the identical Heisenberg-scaling accuracy. Proper interpretation of the super-Heisenberg-scaling accuracy is presented. The scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.
@article{arxiv.1401.5188,
title = {Fitting magnetic field gradient with Heisenberg-scaling accuracy},
author = {Yong-Liang Zhang and Huan Wang and Li Jing and Liang-Zhu Mu and Heng Fan},
journal= {arXiv preprint arXiv:1401.5188},
year = {2014}
}