量子投影滤波
Quantum projection filtering

量子滤波器基于贝叶斯原理, 利用连续弱测量数据给出当前时刻量子系统状态的最优估计, 是量子计算和 量子调控技术中极为重要的一环. 然而, 随着量子系统能级数提高, 量子滤波器的实时计算复杂度呈二次型增长. 本文介绍了一种量子投影滤波方法, 用于减少量子滤波器的实时计算复杂度. 基于量子信息几何方法, 量子轨迹被 限制在了一个由一类非归一化量子密度矩阵组成的子流形中. 量子态从而可通过计算子流形的坐标系统来近似获 得. 仿真实验说明了投影滤波方法的有效性.
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.