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 strategies, 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 strategies can improve parameter precision and extend system coherence time. Then, on the basis of the two control strategies, we propose a practical single-parameter quantum recovery protocol, which includes the preparation of an optimal initial probe state, the active control and optimization of a system evolution process, the design of an adaptive measurement scheme, and the parameter estimation algorithm based on Bayesian estimation theory. In particular, by employing a batch-style adaptive measurement scheme, the parameter recovery is conducted and the effectiveness of the two control strategies is verified.