Validity of Born-Markov master equations for single- and two-qubit systems

V. Vadimov, J. Tuorila, Tuure Orell, J. Stockburger, T. Ala‐Nissila, J. Ankerhold, M. Möttönen
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引用次数: 6

Abstract

The urgent need for reliable simulation tools to match the extreme accuracy needed to control tailored quantum devices highlights the importance of understanding open quantum systems and their modeling. To this end, we compare here the commonly used Redfield and Lindblad master equations against numerically exact results in the case of one and two resonant qubits transversely coupled at a single point to a Drude-cut ohmic bath. All the relevant parameters are varied over a broad range which allows us to give detailed predictions about the validity and physically meaningful applicability of the weak-coupling approaches. We characterize the accuracy of the approximate approaches by comparing the maximum difference of their system evolution superoperators with numerically exact results. After optimizing the parameters of the approximate models to minimize the difference, we also explore if and to what extent the weak-coupling equations can be applied at least as phenomenological models. Optimization may lead to an accurate reproduction of experimental data, but yet our results are important to estimate the reliability of the extracted parameter values such as the bath temperature. Our findings set general guidelines for the range of validity of the usual Born-Markov master equations and indicate that they fail to accurately describe the physics in surprisingly broad range of parameters, in particular at low temperatures. Since quantum-technological devices operate there their accurate modeling calls for a careful choice of methods.
单量子比特和双量子比特系统的Born-Markov主方程的有效性
迫切需要可靠的仿真工具来匹配控制定制量子器件所需的极端精度,这突出了理解开放量子系统及其建模的重要性。为此,我们将常用的Redfield和Lindblad主方程与一个和两个共振量子位在单点横向耦合到德鲁德切割欧姆槽的情况下的数值精确结果进行了比较。所有相关参数都在一个广泛的范围内变化,这使我们能够详细预测弱耦合方法的有效性和物理意义上的适用性。我们通过比较它们的系统演化超级算子的最大差值与数值精确结果来表征近似方法的准确性。在优化近似模型的参数以最小化差异之后,我们还探讨了弱耦合方程是否以及在多大程度上至少可以作为现象学模型应用。优化可能会导致实验数据的准确再现,但我们的结果对于估计提取的参数值(如浴液温度)的可靠性很重要。我们的发现为通常的Born-Markov主方程的有效性范围设定了一般的指导原则,并表明它们无法准确地描述在惊人的广泛参数范围内的物理现象,特别是在低温下。由于量子技术设备在那里运行,它们的精确建模需要仔细选择方法。
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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