测量量子双模型 𝐷(ℤ𝑛) 中拓扑序的方案

拓扑序是超越朗道对称性自发破缺范式的多体量子态，它的典型特征是长程
纠缠、简并的基态和点状激发——任意子。它是理解物质的相和相变的关键，也在高容错的拓扑量子计算中有重要的应用。我们介绍了拓扑序，任意子，还有拓扑序的完备表征，即描述任意子融聚的 𝐹 矩阵和描述编织的 𝑅 矩阵，并以伊辛任意子为例给出了计算任意子 𝐹 矩阵和 𝑅 矩阵的方法。我们介绍了具有拓扑序且严格可解的 Kitaev 量子双模型，并且分别举例介绍了阿贝尔量子双模型和非阿贝尔量子双模型。我们介绍了利用体边对应和在边界上的任意子凝聚来测量 𝑅 矩阵的理论方案，并将其推广到量子双模型 𝐷(ℤ𝑛)（其中 ℤ𝑛 为 𝑛 个元素的循环群）。我们以具有两个 𝑛 能级量子比特的最小量子双模型 𝐷(ℤ𝑛) 为例，讨论了测量 𝑅 矩阵的理论方案。我们还讨论了如何利用两个普通的二能级量子比特来实现一个三能级的量子比特，并且在上面实现 𝑋 和 𝑍 操作，从而能用量子比特来模拟量子双模型 𝐷(ℤ3)；进一步提出具体测量量子双模型 𝐷(ℤ3) 中任意子编织的 𝑅 矩阵的量子
线路和操作步骤。带边界的量子双模型 𝐷(ℤ3) 可以实现通用的拓扑量子计算，我们期待我们的结果为此提供一种可能的实现。

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