单量子比特系统状态的在线估计

针对具有退相干效应与测量反馈随机噪声的随机开放量子系统, 采用对状态影响较弱的连续弱测量在线获取一系列状态的部分信息, 实现量子状态的在线估计.由泡利矩阵构造初始测量算符, 并推导出在线的随时间变化的测量算符; 基于压缩传感理论来减少测量次数; 采用最小二乘优化算法对自由演化中的量子密度矩阵状态进行重构, 完整地给出了量子态在线估计的过程.所提出的在线量子态估计方案, 在一个量子位系统上进行了系统仿真实验.数值仿真实验结果表明, 在满足压缩传感理论的条件下, 仅需2次连续弱测量所得到的测量值之后, 就可以高精度地实现在线变化的单比特量子密度矩阵估计.

On-line State Estimation of One-qubit System

For a stochastic open quantum system with decoherence efiect and measurement feedback random noise, the continuous weak measurement is used to obtain state information on the line to realize the online estimation of quantum state. The Pauli matrix is used to construct the initial measurement operator, and online time-varying measurement operator is derived. The compressed sensing theory is used to reduce the number of measurements. The least squares optimization algorithm is used to reconstruct the state of the quantum density matrix in free evolution, and the whole process of online estimation of quantum state is derived. The proposed online estimation scheme of quantum state is carried out on the one-qubit system. The numerical simulation results show that under the condition of satisfying the compressed sensing theory, the quantum density matrix estimation of high-precision online of one-qubit can be achieved only after 2 measurements of continuous weak measurement.