论文标题
带有非克利福德横向门的四维复合代码
A four-dimensional toric code with non-Clifford transversal gates
论文作者
论文摘要
探索了四维复合代码的设计，目的是找到能够实现逻辑$ \ Mathsf {CCCZ} $ GATE横向实现的晶格。已建立的晶格是八副精彩的晶格，这是四维欧几里得空间的常规镶嵌，其基础的4细胞是八pelex或超甲状要。这不同于常规的4D旋转代码晶格，基于Arperpubic Tessellation，相对于逻辑$ x $和$ z $，这是对称的，并且仅允许实现横向克利福德门。这项工作进一步开发了克利福德层次结构中拓扑维度和横向门之间的既定联系，从而在两个和三个维度中分别概括了已知的设计，用于实现横向$ \ mathsf {cz} $和$ \ mathsf {ccz} $。
The design of a four-dimensional toric code is explored with the goal of finding a lattice capable of implementing a logical $\mathsf{CCCZ}$ gate transversally. The established lattice is the octaplex tessellation, which is a regular tessellation of four-dimensional Euclidean space whose underlying 4-cell is the octaplex, or hyper-diamond. This differs from the conventional 4D toric code lattice, based on the hypercubic tessellation, which is symmetric with respect to logical $X$ and $Z$ and only allows for the implementation of a transversal Clifford gate. This work further develops the established connection between topological dimension and transversal gates in the Clifford hierarchy, generalizing the known designs for the implementation of transversal $\mathsf{CZ}$ and $\mathsf{CCZ}$ in two and three dimensions, respectively.
