Quantum parameter estimation via dispersive measurement in circuit QED

We investigate the quantum parameter estimation in circuit quantum electrodynamics via dispersive measurement. Based on the Metropolis Hastings (MH) algorithm and the Markov chain Monte Carlo (MCMC) integration, a new algorithm is proposed to calculate the Fisher information by the stochastic master equation for unknown parameter estimation. Here, the Fisher information is expressed in the form of log-likehood functions and further approximated by the MCMC integration. Numerical results demonstrate that the single evolution of the Fisher information can probably approach the quantum Fisher information. The same phenomenon is observed in the ensemble evolution in the short time interval. These results demonstrate the effectiveness of the proposed algorithm.