CS (compressive sensing) is adept in the signals of X-ray pulsars. The observation matrix in CS is a core technology. In the CS for X-ray pulsars, the observation matrix has three significant indexes: simple computation, arbitrary size and high precision. To optimize the observation matrix, we propose a quick quantum-based CS, and apply it to the pulsar positioning and velocimetry approach. In the quantum-based CS, the profile dictionary with multi-skewness-degrees and multi-phases are comprised of the X-ray pulsar profiles with multiple phases and skewness degrees. This pulsar profile dictionary is also adopted as the probability amplitude of quantum. The multiple quantum observations of the dictionary form the quantum observation matrix. The quantum observation matrix explores the uncertainty of quantum, and improves its diversity. As the super-resolution sparse recovery, the quantum matched estimation approach provides the pulsar positioning and the pulsar velocimetry simultaneously. Simulation results indicate that compared with the χ² velocimetry, the quick quantum CS-based pulsar positioning and velocimetry has highly accurate and less calculation.

CS（压缩感测）擅长X射线脉冲星的信号。CS中的观察矩阵是一项核心技术。在X射线脉冲星的CS中，观测矩阵具有三个重要指标：计算简单，任意大小和高精度。为了优化观测矩阵，我们提出了一种基于量子的快速CS，并将其应用于脉冲星定位和测速方法。在基于量子的CS中，具有多偏度和多相的轮廓字典由具有多相和偏度的X射线脉冲星轮廓组成。该脉冲星轮廓字典也被用作量子的概率振幅。字典中的多个量子观测形成了量子观测矩阵。量子观测矩阵探索了量子的不确定性，并提高了其多样性。作为超分辨率稀疏恢复，量子匹配估计方法同时提供脉冲星定位和脉冲星测速。仿真结果表明，与χ²测速技术中，基于快速量子CS的脉冲星定位和测速技术具有很高的精确度，并且计算量较少。