Quantum projection filtering for open quantum systems

This paper presents an approximation quantum projection filtering strategy, aiming to reduce the computational cost in calculating the standard quantum filter equation in time. By using a differential geometric approach, the trajectory of the resulting quantum projection filter is constrained to evolve in a finite-dimensional differentiable manifold consisting of an exponential family of quantum density operators. A convenient design of the differentiable manifold is then developed through reduction of the local approximation errors, which allows simplification of the quantum projection filter equations. Finally, simulation results from a two-level quantum system example illustrate the approximation performance of the proposed filtering scheme. The proposed approach is expected to be of practical use in developing more efficient quantum control methods.