$d$-pod 实现非绝热全息量子计算
$d$-pod realization of nonadiabatic holonomic quantum computation
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中文总结 AI 辅助
本文提出将非绝热全息量子计算推广到$d$-pod构型，利用光或微波脉冲实现通用单、双qudit门，并以qutrit为例展示每个门至多两个回路、三个脉冲的紧凑实现。
中文摘要 AI 辅助
全息量子计算（HQC）通过非阿贝尔几何相位实现量子门，提供了一种实验上可及的量子控制方法。虽然非绝热HQC框架已针对编码量子比特的三能级$\Lambda$系统得到广泛发展，但其向高维量子比特（qudit）的系统性扩展在很大程度上仍未探索。在本工作中，我们将非绝热HQC推广到$d$-pod构型，其中单个激发态与$d$个基态耦合，后者构成计算子空间。该方案仅利用作用于囚禁原子或离子的光脉冲或微波脉冲，即可实现通用的全息单量子比特门和双量子比特门，为以最少的脉冲协调实现离散通用门集提供了一条高效途径。作为明确示例，我们详细分析了qutrit（$d=3$）情形，展示了单qutrit和双qutrit全息门的紧凑实现，每个门在由至多三个脉冲生成的Grassmannian中最多需要两个回路。
英文摘要
Holonomic quantum computation (HQC) realizes quantum gates through non-Abelian geometric phases, providing an experimentally accessible approach to quantum control. While the nonadiabatic HQC framework has been extensively developed for three-level $Λ$ systems encoding qubits, its systematic extension to higher-dimensional qudits remains largely unexplored. In this work, we generalize nonadiabatic HQC to a $d$-pod configuration, where a single excited state is coupled to $d$ ground states, the latter forming the computational subspace. This scheme enables universal holonomic single- and two-qudit gates using only optical or microwave pulses on trapped atoms or ions, offering an efficient route to implement a discrete universal gate set with minimal pulse coordination. As an explicit example, we analyze in detail the qutrit ($d=3$) case, demonstrating compact realizations of single- and two-qutrit holonomic gates, each gate requiring at most two loops in the Grassmannian generated by at most three pulses.
发表机构
- Department of Physics and Astronomy, Uppsala University（乌普萨拉大学物理与天文系）
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