改进的迭代收缩阈值算法及其在量子状态估计中的应用

Improved iterative shrinkage threshold algorithm and its application in quantum state estimation

中文关键词  量子状态估计  迭代收缩阈值算法  加速算子  优化算法

英文关键词  quantum state estimation  iterative shrinkage threshold algorithm  acceleration operator  optimization algorithm

中文摘要

      本文将含有稀疏干扰的量子状态估计问题, 转化为考虑量子状态的约束条件下, 分别求解密度矩阵的核范 数, 以及稀疏干扰l1范数的两个子问题的优化问题. 针对迭代收缩阈值算法(ISTA)所存在的收敛速度慢的问题, 通 过在两个子问题的迭代估计中, 引入一个加速算子, 对当前值与前一次值之差进行进一步的补偿, 来提高算法的迭 代速度(FISTA). 并将FISTA算法应用于求解含有稀疏干扰的量子状态估计中. 针对5个量子位的状态估计的仿真实 验, 将FISTA分别与ISTA、交替方向乘子法(ADMM)、不动点方程的ADMM算法(FP–ADMM), 以及非精确的ADMM 算法(I–ADMM)4种优化算法进行性能对比. 实验结果表明, FISTA算法具有更加优越的收敛速度, 并且能够得到更 小的量子状态估计误差.

英文摘要

      In this paper, the quantum state estimation problem with sparse interference is transformed into an optimization problem of solving two sub-problems of the density norm’s kernel norm and the l1 norm of sparse interference under the constraints of quantum states. For the problem of slow convergence for the iterative shrinkage threshold algorithm (ISTA), by introducing an acceleration operator in the iterative estimation of the two sub-problems, the difference between the current value and the previous value is further compensated to improve the iterative speed of the algorithm (FISTA). The FISTA algorithm is applied to solve the quantum state estimation optimization problem with sparse interference. In the state estimation simulation experiment of 5 qubits, the FISTA is compared with the performance of four optimization algorithms: ISTA, alternating direction method of multipliers (ADMM), fixed point ADMM (FP–ADMM) and imprecise ADMM(I–ADMM). The experimental results show that the FISTA algorithm has better convergence and can obtain smaller quantum state estimation errors.