基于卡尔曼滤波的在线量子态估计优化算法

doi:10.12305/j.issn.1001-506X.2021.06.21

摘要/Abstract

摘要：

针对连续弱测量中存在高斯测量噪声的问题, 提出一种基于卡尔曼滤波的在线量子状态估计的预测-修正-投影优化算法。首先，在常规在线卡尔曼滤波算法预测状态时间更新和估计状态测量更新的基础上, 通过增加对量子态的约束条件, 将其应用于在线的量子状态估计中, 将量子态在线估计问题转化为一个带有量子态约束条件的卡尔曼滤波优化问题。其次，通过将待优化问题的求解分解成两个凸优化子问题，一个是基于在线卡尔曼滤波算法求解无约束条件下的量子测量更新问题, 另一个是利用量子约束条件信息, 通过求解矩阵投影问题来获得估计状态。最后，将所提算法应用到4量子位系统状态的在线估计数值实验中, 进行了性能对比实验。实验结果表明, 所提算法具有更优的在线状态估计精度, 并且能够以更少的采样次数和耗时, 实现较高精度的量子状态在线估计。

关键词: 在线量子态估计, 连续弱测量, 约束卡尔曼滤波, 凸优化

Abstract:

Aiming at the problem of Gaussian measurement noise in continuous weak measurement, a prediction correction projection optimization algorithm for online quantum state estimation based on Kalman filter is proposed. Firstly, on the basis of conventional on-line Kalman filter algorithm to predict state time update and estimate state measurement update, by adding constraints on quantum state, it is applied to on-line quantum state estimation, and the problem of on-line quantum state estimation is transformed into a Kalman filter optimization problem with quantum state constraints. Secondly, the optimization problem is decomposed into two convex optimization subproblems. One is based on the online Kalman filter algorithm to solve the quantum measurement update problem under unconstrained conditions, and the other is to obtain the estimated state by solving the matrix projection problem using the quantum constraint information. Finally, the proposed algorithm is applied to the on-line state estimation of 4-qubit system to compare the performance. The experimental results show that the proposed algorithm has better on-line state estimation accuracy, and can achieve higher accuracy on-line quantum state estimation with less sampling times and time-consuming.

Key words: online quantum state estimation, continuous weak measurement, constrained Kalman filter, convex optimization

中图分类号:

TP14

丛爽, 张坤. 基于卡尔曼滤波的在线量子态估计优化算法[J]. 系统工程与电子技术, 2021, 43(6): 1636-1643.

Shuang CONG, Kun ZHANG. Online quantum state estimation optimization algorithm based on Kalman filter[J]. Systems Engineering and Electronics, 2021, 43(6): 1636-1643.

图/表 5

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序列	y₁	y₂	…	y_k
b₁	tr(M₁^†ρ₁)	-	…	-
b₂	tr(M₂^†ρ₂)	tr(M₁^†ρ₂)	…	-
⋮	⋮	⋮	⋱	⋮
b_k	tr(M_k^†ρ_k)	tr(M_k－1^†ρ_k)	…	tr(M₁^†ρ_k)

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