We study quantum magnetometry based on phase-estimation algorithms in a sensor formed by a superconducting qubit coupled to a two-level system (TLS). Using Ramsey interferometry with single-shot binary readout, we construct a precomputed calibration pattern $P_0(f_q,\tau ,{\varphi }_m)$ and implement Bayesian learning. The qubit-TLS exchange reshapes the Ramsey response into a time-dependent structured response with revivals, producing pronounced minima and maxima in the Fisher information. The standard Kitaev algorithm probe weakens information at antirevival times, thereby reducing the net information gain and degrading sensitivity. We further introduce a frequency shift corrected algorithm that improves flux and field sensitivities, expands the dynamical range, and lowers the estimation error rate. Our results show that TLS coupling induces a time-selective metrological response not captured by the effective dephasing time, and that calibration-aware interrogation strategies can mitigate or exploit this structure.

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• Quantum Fisher information
• Quantum algorithms & computation
• Quantum circuits
• Quantum metrology
• Quantum sensing
• Qubits