Clifford gates by code deformation

Topological subsystem color codes add an important feature to the advantages of topological codes: error tracking only involves measuring two local operators in a two-dimensional setting. Unfortunately, currently known methods for computing with them are highly unpractical. We give a mechanism for implementing all Clifford gates by code deformation in a planar setting. In particular, we use twist braiding and express its effects in terms of certain colored Majorana operators.