Quantum projection filtering

All right reserved. A quantum filter extracts the optimal estimate of quantum system states from the past history of weak continuous measurements on a quantum system by using the quantum Bayesian theory. However, the online computation burden of a quantum filter increases quadratically along with the increase of the quantum system dimension. We propose a quantum projection filtering method, aiming to reduce the online computation burden of the quantum filter. By using a differential geometric approach, the trajectory of the resulting quantum filter is constrained to be evolving within a finite-dimensional differentiable submanifold. In other words, the quantum state can be calculated through online calculation of the coordinate system of this submanifold. Simulation results from a two-level quantum system demonstrate the effectiveness of the proposed method.