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

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

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.