用 $(\alpha, \beta)$-超几何统一绝热态转移协议
Unifying adiabatic state-transfer protocols with $(α, β)$-hypergeometries
AI总结：
本文提出 $(\alpha,\beta)$-超几何统一框架，为任意多能级量子系统提供灵活抗噪的绝热动力学实现，并给出保真度损失共振的解析表达式及硅量子点自旋穿梭实验验证。
摘要：
绝热最优控制方案对于推进量子技术的实际实现至关重要。然而，大量可能的绝热协议，加上它们对特定量子系统和功能特定参数范围的依赖，使得在任意操作中辨别它们各自的优势和局限性变得复杂。在这项工作中，我们提供了一个统一的框架，称为 $(\alpha,\beta)$-超几何，它允许对任何多能级量子系统灵活、抗噪声且易于使用地实现强制绝热动力学。此外，该框架通过一个通用代价函数提供了所有绝热协议的全面映射，并给出了绝热动力学的精确解析表征。特别是，我们推导了保真度损失共振的精确表达式，并为任意 $(\alpha,\beta)$ 选择建立了绝热极限下的性能保证。我们还通过解析和数值方法详细讨论了所得脉冲形状的实验可行性。最后，我们测试了我们的方法，用于在具有小谷劈裂的硅量子点中通过自旋穿梭实现相干信息转移的最优控制。
英文摘要：
Adiabatic optimal control schemes are essential for advancing the practical implementation of quantum technologies. However, the vast array of possible adiabatic protocols, combined with their dependence on the particular quantum system and function-specific parameter ranges, complicates the task of discerning their respective strengths and limitations in arbitrary operations. In this work, we provide a unifying framework, called $(α,β)$-hypergeometries, that allows for flexible, noise-resistant, and easy-to-use implementation of enforced adiabatic dynamics for any multi-level quantum system. Moreover, this framework provides a comprehensive mapping of all adiabatic protocols through a universal cost function and offers an exact analytical characterization of the adiabatic dynamics. In particular, we derive precise expressions for infidelity resonances and establish performance guarantees in the adiabatic limit for any choice of $(α,β)$. We also discuss in detail the experimental feasibility of the resulting pulse shapes through analytical and numerical methods. Finally, we test our method for the optimal control of coherent information transfer through spin shuttling in silicon quantum dots with small valley splittings.
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