An Efficient Online Estimation Algorithm for Evolving Quantum States

In this paper, we propose an online optimization algorithm for estimating state density in free evolution quantum systems from noisy continuous weak measurements. The problem is formulated via sparsity-promoting semidefinite programming, and an online quantum state estimation algorithm is developed based on online proximal gradient and alternating direction multiplier method. The proposed algorithm is computationally efficient and further features high robustness to measurement noise. The merits of the approach are illustrated by numerical experiments in 1-, 2-, 3-, and 4-qubit systems.