arXiv 2306.080272023-06quant-ph

带扭曲的 Floquet 码

Floquet codes with a twist

Tyler D. Ellison, Joseph Sullivan, Arpit Dua

备注：: 35+7 pages, 19 figures; v2 corrected typos; v3 corrected fault-tolerance argument, clarified implementation of logical S gate

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AI总结：

本文提出在蜂窝 Floquet 码中通过凝聚缺陷端点构造扭曲缺陷，实现容错量子信息存储与处理，并推广到高维 qudit 的 $\mathbb{Z}_N$ Floquet 码。

摘要：

我们描述了一种在 Hastings 和 Haah 的蜂窝 Floquet 码中创建扭曲缺陷的方法。具体而言，我们在凝聚缺陷的端点处构造扭曲缺陷，这些凝聚缺陷是通过沿一维路径凝聚涌现费米子而构建的。我们认为扭曲缺陷可用于容错地存储和处理量子信息，并证明通过在具有边界的系统上制备扭曲缺陷，我们获得了 $\mathbb{Z}_2$ Floquet 码的平面变体。重要的是，我们的扭曲缺陷构造保持了六边形晶格的连通性，仅需要 2 体测量，并保留了测量调度的三轮周期。我们进一步将扭曲缺陷推广到定义在 $N$ 维 qudit 上的 $\mathbb{Z}_N$ Floquet 码。作为附带内容，我们使用 $\mathbb{Z}_N$ Floquet 码和凝聚缺陷来定义瞬时稳定子群由某些阿贝尔扭曲量子双模型（twisted quantum doubles）的拓扑序所表征的 Floquet 码。

英文摘要：

We describe a method for creating twist defects in the honeycomb Floquet code of Hastings and Haah. In particular, we construct twist defects at the endpoints of condensation defects, which are built by condensing emergent fermions along one-dimensional paths. We argue that the twist defects can be used to store and process quantum information fault tolerantly, and demonstrate that, by preparing twist defects on a system with a boundary, we obtain a planar variant of the $\mathbb{Z}_2$ Floquet code. Importantly, our construction of twist defects maintains the connectivity of the hexagonal lattice, requires only 2-body measurements, and preserves the three-round period of the measurement schedule. We furthermore generalize the twist defects to $\mathbb{Z}_N$ Floquet codes defined on $N$-dimensional qudits. As an aside, we use the $\mathbb{Z}_N$ Floquet codes and condensation defects to define Floquet codes whose instantaneous stabilizer groups are characterized by the topological order of certain Abelian twisted quantum doubles.

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