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Precise measurement of magnetic fields is essential for various applications,such as fundamental physics, space exploration, and biophysics. Although recentprogress in quantum engineering has assisted in creating advanced quantummagnetometers, there are still ongoing challenges in improving their efficiencyand noise resistance. This study focuses on using symmetric graph stateresources for quantum magnetometry to enhance measurement precision byanalyzing the estimation theory under Markovian and non-Markovian noise models.The results show a significant improvement in estimating both single andmultiple Larmor frequencies. In single Larmor frequency estimation, the quantumFisher information spans a spectrum from the standard quantum limit to theHeisenberg limit within a periodic range of the Larmor frequency, and in thecase of multiple Larmor frequencies, it can exceed the standard quantum limitfor both Markovian and non-Markovian noise. This study highlights the potentialof graph state-based methods for improving magnetic field measurements undernoisy environments.

Harnessing graph state resources for robust quantum magnetometry under noise