Real-time parameter estimation for two-qubit systems based on hybrid control

In this paper, we consider the real-time parameter estimation problem for a ZZ-coupled system composed of two qubits in the presence of spontaneous emission. To enhance the estimation precision of the coupling coefficient, we first propose two different control schemes, where the first one is feedback control based on quantum-jump detection, and the second one is hybrid control combining Markovian feedback and Hamiltonian control. The simulation results show that compared with free evolution, both control schemes can improve parameter precision and extend system coherence time. Next, on the basis of the two control schemes, we propose a practical single-parameter quantum recovery protocol based on Bayesian estimation theory. In this protocol, by employing batch-style adaptive measurement rules, parameter recovery is conducted to verify the effectiveness of both control schemes.