Color codes with domino twists: construction, logical measurements, and computation

Abstract

Twists are defects that are used to encode and process quantum information in topological codes like surface and color codes. Color codes can host three basic types of twists, namely charge-permuting, color-permuting, and domino twists. In this paper, we study domino twists from the viewpoint of computation. Specifically, we give a systematic construction for domino twists in qubit color codes. We also present protocols for measurement of logical qubits. Finally, we show that all Clifford gates can be implemented by braiding twists.