<p>We develop the quantum approach to magnetometry utilizing phase estimation algorithms, demonstrating improvements in the estimation of magnetic flux in both precision and dynamical range. We propose the modifications to conventional algorithms including the signal modulation and proximity time measurements. We demonstrate that our approach extends the dynamical range and improves the precision of magnetic flux detection. We show that our approach enhances performance of superconducting qubits and enables higher information gain without compromising dynamical range, paving the way toward achieving the Heisenberg limit. Combining adaptive algorithms with device-specific calibration, our methods bridge the gap between theoretical advancements and practical quantum sensing applications, offering a powerful framework for metrology using superconducting qubits.</p>