基于Kraus映射演化的开放量子系统控制景观的优化搜索
Optimization search effort over the control landscapes for open quantum systems with Kraus-map evolution
摘要：
量子控制景观被定义为作为控制变量的函数的目标可观测$Θ$的期望值。在这项工作中，控制景观的开放量子系统的Kraus映射演化进行了分析。Kraus映射被用作将初始密度矩阵$ρ_{\rm i}$转换为最终密度矩阵以最大化可观测$Θ$的期望值的控制。次优的局部最大值的相关控制景观的情况下，数值说明。根据系统$N$、初始状态$ρ_{\rm i}$和目标可观测值$Θ$的维度来分析优化搜索努力的依赖性。结果发现，如果在$ρ_{\rm i}$的非零特征值的数量保持不变，搜索工作不表现出任何显着的依赖于$N$。如果$ρ_{\rm i}$没有零特征值，则计算复杂度和所需的搜索工作量随着$N$而增加。顶部歧管的尺寸（即，最大化目标的Kraus算子集合）与优化搜索效率正相关。在完全可控的假设下，非相干控制建模的Kraus映射被发现是更有效地达到相同的目标值比相干控制建模的酉映射。数值模拟也进行了控制景观与线性约束的可用克劳斯地图，次优的最大值没有显示这些景观。
英文摘要：
A quantum control landscape is defined as the expectation value of a target observable $Θ$ as a function of the control variables. In this work control landscapes for open quantum systems governed by Kraus map evolution are analyzed. Kraus maps are used as the controls transforming an initial density matrix $ρ_{\rm i}$ into a final density matrix to maximize the expectation value of the observable $Θ$. The absence of suboptimal local maxima for the relevant control landscapes is numerically illustrated. The dependence of the optimization search effort is analyzed in terms of the dimension of the system $N$, the initial state $ρ_{\rm i}$, and the target observable $Θ$. It is found that if the number of nonzero eigenvalues in $ρ_{\rm i}$ remains constant, the search effort does not exhibit any significant dependence on $N$. If $ρ_{\rm i}$ has no zero eigenvalues, then the computational complexity and the required search effort rise with $N$. The dimension of the top manifold (i.e., the set of Kraus operators that maximizes the objective) is found to positively correlate with the optimization search efficiency. Under the assumption of full controllability, incoherent control modelled by Kraus maps is found to be more efficient in reaching the same value of the objective than coherent control modelled by unitary maps. Numerical simulations are also performed for control landscapes with linear constraints on the available Kraus maps, and suboptimal maxima are not revealed for these landscapes.
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