用表面码戳孔和偷工减料来实现克利福德门
Poking holes and cutting corners to achieve Clifford gates with the surface code
摘要：
表面码是目前实现容错量子计算的主要方案。在其优势是过多的已知方式，容错克利福德操作可以执行，即通过变形的拓扑结构的表面，通过融合和分裂的代码，甚至通过编织工程马约拉纳模式使用扭曲缺陷。在这里，我们提出了一个统一的框架来描述这些方法，可以用来更好地比较不同的计划，并促进混合计划的设计。我们的统一包括识别扭曲缺陷的角落的平面代码。这种识别使我们能够通过代码变形交换平面代码的角来执行单量子位Clifford门。我们分析的方式，不同的计划可以结合起来，并提出了一个新的逻辑编码。我们还展示了如何所有的克利福德门可以实现与平面代码没有损失的距离使用代码变形，从而提供了一个有吸引力的替代辅助介导的计划来完成克利福德组与晶格手术。
英文摘要：
The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the topology of the surface, by the fusion and splitting of codes and even by braiding engineered Majorana modes using twist defects. Here we present a unified framework to describe these methods, which can be used to better compare different schemes, and to facilitate the design of hybrid schemes. Our unification includes the identification of twist defects with the corners of the planar code. This identification enables us to perform single-qubit Clifford gates by exchanging the corners of the planar code via code deformation. We analyse ways in which different schemes can be combined, and propose a new logical encoding. We also show how all of the Clifford gates can be implemented with the planar code without loss of distance using code deformations, thus offering an attractive alternative to ancilla-mediated schemes to complete the Clifford group with lattice surgery.
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