Quantum state reconstruction method and system based on compressive sensing

The invention discloses a quantum state reconstruction method and system based on compressive sensing. The quantum state reconstruction method based on compressive sensing integrates an ADMM algorithm and an ISTA algorithm, and an auxiliary variable e is introduced in the iterative process so that the quantum state reconstruction problem is solved under an ADMM algorithm framework, and more accurate solution can be rapidly obtained. In addition, a conventional calculation sequence is changed in the mode of adding brackets three times in the density matrix updating process, so that the computational complexity is greatly reduced, and the operation times are greatly decreased, the time required by the quantum state reconstruction process is shortened, and the operating efficiency is improved. Further, a measurement matrix A of M * d2 is directly constructed by adopting the quantum state reconstruction method based on compressive sensing, a more general convex optimization model considering that white gaussian noise is contained in a measured value is adopted, fixed step length for lagrangian multiplier updating is changed into adjustable step length, the convergence speed is improved, and the number of iterations and computation time are decreased.