Fluxonium-based superconducting qubit magnetometer: Optimization of phase estimation algorithms

High-precision magnetometers have found wide applications in medicine, geological exploration, material property studies, and other fields of human activity. Recently, there has been significant development in magnetometers based on the evolution of quantum system states under the influence of an external magnetic field. A notable example of such a quantum system is the fluxonium superconducting qubit. In this paper, we evaluate the performance of a low-frequency magnetic field sensor based on the fluxonium qubit. The analysis utilizes parameters from qubits implemented by various experimental groups. We compare the performance of a fluxonium-based magnetometer with that of superconducting quantum interference devices. Our calculations show that fluxonium-based magnetometers are capable of high-precision measurements and that the high intrinsic inductance of the fluxonium loop allows efficient coupling with auxiliary antennas. Moreover, we propose the algorithm upgrade for low-frequency magnetic field measurements using qubits, which could enhance measurement accuracy by approximately a factor of two compared to existing qubit-based algorithms.