Abstract

In this work, we consider a pair of qubits controlled by coherent and incoherent controls. The dynamics of the two-qubit system is driven by a Gorini–Kossakowsky–Sudarchhan–Lindblad master equation where coherent control enters into the Hamiltonian and incoherent control inters into both the Hamiltonian (via Lamb shift) and the dissipative superoperator. Two classes of interaction between the system and the coherent field are considered. For this system, we analyze the control problem of generating a given target density matrix which is formulated as minimizing the Hilbert–Schmidt distance between the final density matrix and the target density matrix. Incoherent control is modeled as a sum of constant in time Gaussians with centers related with the transitions frequencies between the energy levels of the qubits. Coherent control in general formulation is considered as measurable function and in numerical experiments as piecewise constant function with constraints on magnitudes and variations. Finite-dimensional numerical optimization is performed using the dual annealing method; the corresponding results are described for some initial and target density matrices and for some set of the parameters of the control problem.

中文翻译：

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使用相干和非相干控制为两个量子位生成密度矩阵

摘要

在这项工作中，我们考虑由相干和非相干控制控制的一对量子位。双量子比特系统的动力学由 Gorini-Kossakowsky-Sudarchhan-Lindblad 主方程驱动，其中相干控制进入哈密顿量，非相干控制进入哈密顿量（通过兰姆位移）和耗散超级算子。考虑了系统和相干场之间的两类相互作用。对于这个系统，我们分析了生成给定目标密度矩阵的控制问题，该矩阵被公式化为最小化最终密度矩阵和目标密度矩阵之间的希尔伯特-施密特距离。非相干控制被建模为时间高斯常数的总和，其中心与量子位能级之间的跃迁频率相关。一般公式中的相干控制被认为是可测量的函数，在数值实验中被认为是具有幅度和变化约束的分段常数函数。采用双重退火法进行有限维数值优化；描述了一些初始和目标密度矩阵以及控制问题的一些参数集的相应结果。