Quantum state filter and a related method

Abstract

The invention discloses a quantum state filter and a related method. The proximal Jacobian ADMM algorithm is applied to the reconstruction of high qubit states based on squeezed sensing to ensure thatthe reconstructed density matrix satisfies the constraint of quantum states. The algorithm can find more accurate solutions more quickly. The algorithm adds a nearest neighbor term to each sub-problem to obtain a closed-form solution, avoids large-scale matrix operation and greatly reduces the computational complexity. At the same time, the Lagrangian multiplier is updated with adjustable step size to accelerate the convergence rate, and the conditions satisfying the convergence of the algorithm are given to provide a basis for the parameter selection. The filter can realize the simultaneousestimation of the quantum state with state sparse disturbance and Gaussian noise and its sparse disturbance and Gaussian noise with high precision.

Description

technical field [0001] The invention relates to the technical field of quantum state estimation, in particular to a quantum state filter and related methods. Background technique [0002] The state density matrix ρ of a quantum system of n qubits is a d×d(d=2 n ) matrix with d×d=2n×2n=4n parameters, so the quantity of quantum state parameters to be estimated increases exponentially with the growth of n, in other words, a standard quantum state estimation needs O(d 2 ) times the measurement configuration. In practical experiments, the quantum state that people are interested in is often a pure state or an approximate pure state, and at this time ρ is a low-rank Hermitian matrix with rank r. Using this prior information, people apply the compressive sensing theory proposed by Candes, Donaho et al. in 2006 to quantum state estimation: first, through a measurement matrix A, the original signal is projected into a low-dimensional space; then by solving an optimization The prob...

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Problems solved by technology

[0004] For problem 2), the convex optimization algorithm based on compressed sensing quantum state estimation, because the parameters involved are of large dimension, it is difficult for general algorithms to solve effectively

However, in Li's algorithm, a large number of high-order matrix inversion operations cause the algorithm to take a long time. Taking qubit n=7 as an example, on a machine with Intel XeonE5-2407CPU, 2 cores, main frequency 2.4GHz, and memory 16G It takes nearly 3 hours to reconstruct the density matrix with a correct rate of 92.43%

In addition, in the optimization problem defined by Li, when the density matrix contains sparse interference and the measurement value contains noise, the optimization algorithm based on this problem becomes more difficult to reconstruct and the effect becomes worse

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