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

TL;DR

This paper systematically constructs domino twists in qubit color codes, enabling logical qubit measurements and demonstrating that all Clifford gates can be implemented through braiding twists, advancing topological quantum computation.

Contribution

It introduces a systematic construction of domino twists in qubit color codes and protocols for logical qubit measurement, showing their use in implementing Clifford gates.

Findings

Systematic construction of domino twists in qubit color codes.

Protocols for measurement of logical qubits using twists.

Implementation of all Clifford gates via braiding twists.

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 viz., 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.