Design of a Linear Quantum Projection Filter

In order to reduce the computational cost for online calculation of the quantum filter, in this paper, a linear quantum projection filtering scheme is developed by projecting the time evolution trajectory of quantum system state onto a lower-dimensional linear submanifold spanned by a set of basis matrices. The lower-dimensional submanifold is obtained through an extended singular value decomposition algorithm. Compared with the existing works on quantum projection filtering, the proposed approach requires no prior knowledge on the structure of the submanifold, and thus can be used to deal with general open quantum systems. Simulation results demonstrate that the proposed linear projection filter is able to approximate the high-dimensional quantum filter within acceptable accuracy.