引用本文: | 丛爽,汪涛,张坤.带有自适应学习速率的矩阵指数梯度在线量子态估计算法[J].控制理论与应用,2021,38(8):1188~1196.[点击复制] |
CONG Shuang,WANG Tao,ZHANG Kun.Online quantum state estimation optimization algorithm with adaptive learning rate matrix exponentiated gradient[J].Control Theory and Technology,2021,38(8):1188~1196.[点击复制] |
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带有自适应学习速率的矩阵指数梯度在线量子态估计算法 |
Online quantum state estimation optimization algorithm with adaptive learning rate matrix exponentiated gradient |
摘要点击 1569 全文点击 540 投稿时间:2020-07-08 修订日期:2020-12-14 |
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DOI编号 10.7641/CTA.2020.00425 |
2021,38(8):1188-1196 |
中文关键词 量子态在线估计 连续弱测量 矩阵指数梯度算法 自适应学习速率 |
英文关键词 online quantum state estimation continuous weak measurement matrix exponentiated gradient algorithm adaptive learning rate |
基金项目 国家自然科学基金项目(61973290)资助. |
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中文摘要 |
针对连续弱测量中存在高斯噪声的情况, 提出一种带有自适应学习速率的矩阵指数梯度在线量子态估计
算法. 将量子态估计问题转化为含量子约束的凸优化问题, 通过引入Von Neumann散度(量子相对熵), 在一阶最优条
件下, 推导出指数型的量子态迭代公式, 保证量子态密度矩阵的半正定性. 再通过对迭代结果进行迹为1的投影, 得
到最终的量子态估计值. 同时在迭代公式中设计自适应的学习速率, 进一步加快算法的收敛速度. 将所提出的算法
分别在1, 2, 3和4个量子位系统上, 进行了在线量子态估计的数值仿真实验, 并与现有的在线量子态估计算法进行了
性能对比. 实验结果表明, 所提出的算法具有更好的快速收敛性, 以及更高的状态估计精度. |
英文摘要 |
For the presence of Gaussian noise in the continuous weak measurement process, an online quantum state
estimation optimization algorithm with adaptive learning rate matrix exponentiated gradient (ALR–MEG) is proposed. The
quantum state online estimation problem is transformed into convex optimization problem with quantum state constraints,
and Von Neumann divergence (quantum relative entropy) is introduced into the problem. Under the first-order optimal
condition, an exponential quantum state iteration formula is derived, which ensures the positive semi-definite of the quantum
state density matrix, and then by projecting the iteration result with one trace, the final quantum state estimate is obtained.
At the same time, the adaptive learning rate is designed in the iterative formula to accelerate the convergence speed of the
algorithm. The proposed algorithm is applied on the 1, 2, 3 and 4 qubit systems, and numerical simulation experiments
of online quantum state estimation are carried out. The performance is compared with the existing online quantum state
estimation algorithm. The results show that the proposed algorithm has better rapid convergence, higher state estimation
accuracy. |
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