  Precise measurement of magnetic fields is essential for various applications,
such as fundamental physics, space exploration, and biophysics. Although recent
progress in quantum engineering has assisted in creating advanced quantum
magnetometers, there are still ongoing challenges in improving their efficiency
and noise resistance. This study focuses on using symmetric graph state
resources for quantum magnetometry to enhance measurement precision by
analyzing the estimation theory under Markovian and non-Markovian noise models.
The results show a significant improvement in estimating both single and
multiple Larmor frequencies. In single Larmor frequency estimation, the quantum
Fisher information spans a spectrum from the standard quantum limit to the
Heisenberg limit within a periodic range of the Larmor frequency, and in the
case of multiple Larmor frequencies, it can exceed the standard quantum limit
for both Markovian and non-Markovian noise. This study highlights the potential
of graph state-based methods for improving magnetic field measurements under
noisy environments.
