Abstract:

Aiming at the problem of Gaussian measurement noise in continuous weak measurement, a prediction correction projection optimization algorithm for online quantum state estimation based on Kalman filter is proposed. Firstly, on the basis of conventional on-line Kalman filter algorithm to predict state time update and estimate state measurement update, by adding constraints on quantum state, it is applied to on-line quantum state estimation, and the problem of on-line quantum state estimation is transformed into a Kalman filter optimization problem with quantum state constraints. Secondly, the optimization problem is decomposed into two convex optimization subproblems. One is based on the online Kalman filter algorithm to solve the quantum measurement update problem under unconstrained conditions, and the other is to obtain the estimated state by solving the matrix projection problem using the quantum constraint information. Finally, the proposed algorithm is applied to the on-line state estimation of 4-qubit system to compare the performance. The experimental results show that the proposed algorithm has better on-line state estimation accuracy, and can achieve higher accuracy on-line quantum state estimation with less sampling times and time-consuming.

Key words: online quantum state estimation, continuous weak measurement, constrained Kalman filter, convex optimization