In this paper, we propose an online state tomography method for N-qubit quantum system based on the continuous weak measurement and compressed sensing (CS). The quantum system is described by stochastic master equation. The continuous weak measurement operators for the N-qubit quantum system, which are indirectly acted on the quantum system, are derived according to the measurement operator results of two-level quantum system. The online time-varying measurement operators are obtained by means of the dynamic evolution equation of the system. The quantum state is online estimated by solving the optimization problem of minimizing the two-norm with the positive definite constraints of density matrix, and we use the nonnegative least squares algorithm to solve the optimization problem. CS theory is used to reduce the number of the measurements in the process of online state estimation. In the numerical experiments, we study the effects of external control field, measurement rate and the different numbers of qubits on the performance in the proposed method. The minimum required numbers of measurements for 2, 3, 4 and 5 qubits are found. The normalized distance and fidelity of our proposed method can achieve satisfying accuracy with small number of measurements.

中文翻译：

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通过连续弱测量和压缩传感对 N 量子位进行在线量子态断层扫描

在本文中，我们提出了一种在线状态断层扫描方法ñ-基于连续弱测量和压缩感知（CS）的量子比特量子系统。量子系统由随机主方程描述。连续弱测量算子ñ根据二能级量子系统的测量算子结果推导出间接作用于量子系统的-qubit量子系统。通过系统的动态演化方程得到在线时变测量算子。通过求解密度矩阵正定约束的二范数最小化优化问题在线估计量子态，并采用非负最小二乘算法求解优化问题。CS理论用于减少在线状态估计过程中的测量次数。在数值实验中，我们研究了外部控制场、测量速率和不同数量的量子比特对所提出方法的性能的影响。2、3、找到了 4 和 5 个量子比特。我们提出的方法的归一化距离和保真度可以通过少量测量达到令人满意的精度。