Quantum state reconstruction method and system based on compressive sensing

Abstract

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.

Description

technical field [0001] The present application relates to the technical field of quantum state reconstruction, and more specifically, relates to a quantum state reconstruction method and system based on compressive sensing. Background technique [0002] The state density matrix ρ of a quantum system with n qubits (qubits) is a d×d (where d=2 n ) matrix with 2 n ×2 n =4 n parameters. Therefore, the number of quantum state parameters to be estimated when performing quantum state estimation of the quantum system increases exponentially with the growth of n. In other words, a standard quantum state estimation requires O(d 2 ) times the measurement configuration. [0003] In practical applications, the quantum state that people are interested in is often a pure state or an approximate pure state, and the state density matrix ρ is a low-rank Hermitian matrix with rank r. Using this prior information, people apply the compressive sensing theory proposed by Candes and Donaho e...

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Problems solved by technology

For the second problem, the prior art discloses a method of using the Alternating Direction Method of Multipliers (ADMM) to solve the quantum state reconstruction problem based on compressive sensing, and obtains a fast and robust Quantum state reconstruction method, but because there are still a large number of high-order matrix inversion operations in this method, it takes a long time and the efficiency is low

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