Clifford gates by code deformation

Abstract

Topological subsystem color codes add to the advantages of topological codes\nan important feature: error tracking only involves measuring 2-local operators\nin a two dimensional setting. Unfortunately, known methods to compute with them\nwere highly unpractical. We give a mechanism to implement all Clifford gates by\ncode deformation in a planar setting. In particular, we use twist braiding and\nexpress its effects in terms of certain colored Majorana operators.\n