Using and Optimizing Time-Dependent Decoherence Rates and Coherent Control for a Qutrit System

Pub Date : 2024-07-11 DOI:10.1134/s0081543824010152

Oleg V. Morzhin, Alexander N. Pechen

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Abstract

We consider an open qutrit system in which the evolution of the density matrix \(\rho(t)\) is governed by the Gorini–Kossakowski–Sudarshan–Lindblad master equation with simultaneous coherent (in the Hamiltonian) and incoherent (in the dissipation superoperator) controls. To control the qutrit, we propose to use not only coherent control but also generally time-dependent decoherence rates which are adjusted by the so-called incoherent control. In our approach, the incoherent control makes the decoherence rates time-dependent in a specific controlled manner and within a clear physical mechanism. We consider the problem of maximizing the Hilbert–Schmidt overlap between the final state \(\rho(T)\) of the system and a given target state \(\rho_{\text{target}}\), as well as the problem of minimizing the squared Hilbert–Schmidt distance between these states. For both problems, we perform their realifications, derive the corresponding Pontryagin functions, adjoint systems (with two variants of transversality conditions for the two terminal objectives), and gradients of the objectives, and adapt the one-, two-, and three-step gradient projection methods. For the problem of maximizing the overlap, we also adapt the regularized first-order Krotov method. In the numerical experiments, we analyze first the operation of the methods and second the obtained control processes, in respect of considering the environment as a resource via incoherent control.

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使用并优化 Qutrit 系统随时间变化的退相干率和相干控制

摘要我们考虑了一个开放的qutrit系统，在这个系统中，密度矩阵\(\rho(t)\)的演化受Gorini-Kossakowski-Sudarshan-Lindblad主方程控制，同时存在相干（在哈密顿中）和非相干（在耗散超算子中）控制。为了控制 qutrit，我们建议不仅使用相干控制，而且使用一般随时间变化的退相干率，通过所谓的非相干控制进行调整。在我们的方法中，非相干控制使退相干率以特定的受控方式和明确的物理机制随时间变化。我们考虑的问题是最大化系统最终状态（\rho(T)\）与给定目标状态（\rho_\{text{target}}\）之间的希尔伯特-施密特重叠，以及最小化这些状态之间的希尔伯特-施密特距离平方。对于这两个问题，我们都对其进行了求解，得出了相应的庞特里亚金函数、邻接系统（两个终端目标的横向条件有两种变体）和目标梯度，并调整了一步、两步和三步梯度投影法。对于重叠最大化问题，我们还采用了正则化一阶 Krotov 方法。在数值实验中，我们首先分析了这些方法的运行情况，其次分析了通过不连贯控制将环境视为资源时所获得的控制过程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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