Abstract: The size of the quantum measurement matrix in the Quantum based CS (QCS) of X-ray pulsar positioning and velocimetry method is large. To reduce calculation time, a fast Quantum-CS method based on the Sparrow Search Algorithm optimization (SSA-QCS) was proposed and applied to the pulsar positioning and velocimetry. The quantum measurement mother matrix in QCS was divided into multiple sub-matrices. The quantum measurement sub-matrices were selected from the quantum measurement mother matrix through SSA. With the location of every sparrow corresponding to the combination of quantum measurement sub-matrices, with the estimation errors of the positioning and velocimetry in QCS as the object of the fitness function, through iterations, the optimal combination of the quantum measurement sub-matrices was obtained, forming a small-sized and high-performance quantum measurement matrix. Simulation results show that the SSA-QCS has a lower calculation cost and higher accuracy compared with the QCS. SSA-QCS can reach high-accuracy and real-time X-ray pulsar positioning and velocimetry.