Magnetic Field Detection Using a Two-Qubit System Under Noisy Heisenberg Interaction

We propose a method to design a magnetic field detector using a noisy two-qubit system. The system evolves under a noisy Heisenberg interaction Hamiltonian, and we investigate its behavior by calculating both the $l_1$-norm of quantum coherence and the return probability in the presence and absence of an external magnetic field. We allow for decoherence modeled by quasi-static charge noise in the exchange coupling of the two-qubit system and find that, while the magnetic field does not significantly influence the decoherence process, it introduces a distinct oscillation in the return probability over time. Importantly, the oscillation frequency is directly proportional to the strength of the applied magnetic field, providing a clear signature that can be used for magnetic field detection. These results point towards the feasibility of realizing a practical quantum-based magnetic field detector, with the ability to operate under noisy conditions while maintaining sensitivity to the field strength.