Efficient and Fast Optimization Algorithms for Quantum State Filtering and Estimation

In this paper, based on Alternating Direction Multiplier Method (ADMM) and Compressed Sensing (CS), we develop three types of novel convex optimization algorithms for the quantum state estimation and filtering. Considering sparse state disturbance and measurement noise simultaneously, we propose a quantum state filtering algorithm. At the same time, the quantum state estimation algorithms for either sparse state disturbance or measurement noise are proposed, respectively. Contrast with other algorithms in literature, simulation experiments verify that all three algorithms have low computational complexity, fast convergence speed and high estimation accuracy at lower measurement rates.