论文标题

Krotov方法控制开放量子系统的有效性

Effectiveness of the Krotov method in controlling open quantum systems

论文作者

Fonseca, Marllos E., Fanchini, Felipe F., de Lima, Emanuel F., Castelano, Leonardo K.

论文摘要

我们将Krotov方法应用于开放和封闭的量子系统,目的是在存在外部环境的情况下找到优化的控件来操纵量子/QUTRIT系统。在统一优化的情况下,首先将Krotov方法应用于量子系统,忽略了其与环境的相互作用。然后,使用统一优化的最终控件与环境噪声一起驱动系统。在非统一优化的情况下,Krotov方法已经在优化过程中考虑了噪声。我们考虑两个不同的计算任务:目标状态准备和量子门实现。这些任务是在简单的Qubit/Qutrit系统以及呈现泄漏状态的系统中执行的。对于状态准备案例,来自非整体优化的控件优于单位优化的控件。但是,正如我们在这里显示的那样,对于量子门的实现并不总是如此。在某些情况下,与非统一优化相比,统一优化的性能同样出色。我们验证这些情况是否对应于缺乏泄漏状态或散布在系统上(包括非计算水平)的耗散效应。在这种情况下,量子门实施必须涵盖整个希尔伯特空间,并且没有办法躲避耗散。另一方面,如果包含计算水平及其补体的子空间会受到耗散的不同影响,则非整体优化将有效。

We apply the Krotov method for open and closed quantum systems with the objective of finding optimized controls to manipulate qubit/qutrit systems in the presence of the external environment. In the case of unitary optimization, the Krotov method is first applied to a quantum system neglecting its interaction with the environment. The resulting controls from the unitary optimization are then used to drive the system along with the environmental noise. In the case of non-unitary optimization, the Krotov method already takes into account the noise during the optimization process. We consider two distinct computational task: target-state preparation and quantum gate implementation. These tasks are carried out in simple qubit/qutrit systems and also in systems presenting leakage states. For the state-preparation cases, the controls from the non-unitary optimization outperform the controls from the unitary optimization. However, as we show here, this is not always true for the implementation of quantum gates. There are some situations where the unitary optimization performs equally well compared to the non-unitary optimization. We verify that these situations corresponds to either the absence of leakage states or to the effects of dissipation being spread uniformly over the system, including non-computational levels. For such cases, the quantum gate implementation must cover the entire Hilbert space and there is no way to dodge dissipation. On the other hand, if the subspace containing the computational levels and its complement are differently affected by dissipation, the non-unitary optimization becomes effective.

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