IQI Weekly Seminar

Abstract: 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 is required to better compare different schemes, and to facilitate the design of hybrid schemes. Novel to our unification is the identification of twist defects with the corners of the planar code. This identification enables us to find new ways of performing single-qubit Clifford gates by exchanging the corners of the planar code via code deformation. We analyse the ways in which all of the different schemes can be combined, and propose a novel hybrid encoding. We also show how all ofthe Clifford gates can be implemented on a single code without loss of distance, thus offering an attractive alternative to ancilla-mediated schemes to complete the Clifford group with lattice surgery.