  The aim of quantum metrology is to estimate target parameters as precisely as
possible. In this paper, we consider quantum metrology based on
symmetry-protected adiabatic transformation. We introduce a ferromagnetic Ising
model with a transverse field as a probe and consider the estimation of a
longitudinal field. Without the transverse field, the ground state of the probe
is given by the Greenberger-Horne-Zeilinger state, and thus the Heisenberg
limit estimation of the longitudinal field can be achieved through parity
measurement. In our scheme, full information of the longitudinal field encoded
on parity is exactly mapped to global magnetization by symmetry-protected
adiabatic transformation, and thus the parity measurement can be replaced with
global magnetization measurement. Moreover, this scheme requires neither
accurate control of individual qubits nor that of interaction strength. We
discuss the effects of the finite transverse field and nonadiabatic transitions
as imperfection of adiabatic transformation. By taking into account finite time
duration for state preparation, sensing, and readout, we also compare
performance of the present scheme with a classical scheme in the absence and
presence of dephasing.
