  We propose a dynamic quantum sensing scheme by using a quantum many-spin
system composed of a central spin interacting with many surrounding spins.
Starting from a generalized Ising ring model, we investigate the error
propagation formula of the central spin and it indicates that Heisenberg
scaling can be reached while the probe state only needs to be a product state.
Particularly, we derive an analytical form of the dynamic quantum Fisher
information in a limit case, which explicitly exhibits the Heisenberg scaling.
By comparing with numerical results, we demonstrate that the general case can
be well approximated by the analytical result when the coupling strength among
the surrounding spins is much weaker than the coupling strength between the
central and surrounding spins. This analytic result guides us to find the
appropriate probe state and the proper measurement time, to achieve the
Heisenberg scaling in realistic situations. Furthermore, we investigate various
effects which are important in practical quantum systems, including the central
spin Zeeman term, the anisotropy of the hyperfine interaction and the
inhomogeneity of the hyperfine coupling strength. Our result indicates that the
dynamic quantum-enhanced sensing scheme seems feasible in realistic quantum
central spin systems, like semiconductor quantum dots.
