We study the dynamics of a two-level crossing model with a polynomial modification of the linear Landau–Zener tunneling. For a cubic modification, we express the non-adiabatic transition amplitudes analytically via the bi-confluent Heun functions. We find a closed-form series expression of the transition probability at the long time limit, and derive tractable approximate formulas to the state populations in a large part of the parameter space. The analytical approximations are validated by comparison with numerical results. Finally, we discuss the application to fast high fidelity quantum gates in quantum computing.

中文翻译：

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三次平交模型动力学的解析近似

我们研究了线性Landau-Zener隧道的多项式修改的两层交叉模型的动力学。对于三次修改，我们通过双合流Heun函数解析地表示非绝热过渡幅度。我们找到了很长一段时间内转移概率的封闭形式的级数表达式，并在很大一部分参数空间中导出了状态种群的易于处理的近似公式。通过与数值结果进行比较，可以验证分析近似值。最后，我们讨论了快速高保真量子门在量子计算中的应用。