Quantum computation with charge-and-color permuting twists in qudit color codes

TL;DR

This paper introduces the first study of twists in qudit color codes over odd prime alphabets, enabling quantum computation through charge-and-color permuting twists.

Contribution

It systematically constructs twists in qudit color codes that permute charge and color, and develops protocols for implementing generalized Clifford gates.

Findings

First construction of twists in qudit color codes

Protocols for implementing generalized Clifford gates

Mapping between Pauli operators and lattice strings

Abstract

Twists are defects in the lattice which can be utilized to perform computations on encoded data. Twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes and qubit subsystem color codes. They are known to exhibit projective non-Abelian statistics which is exploited to perform encoded gates. In this paper, we initiate the study of twists in qudit color codes over odd prime alphabet. To the best of our knowledge, this is the first study of twists in qudit color codes. Specifically, we present a systematic construction of twists in qudit color codes that permute both charge and color of the excitations. We also present a mapping between generalized Pauli operators and strings in the lattice. Making use of the construction, we give protocols to implement generalized Clifford gates using charge-and-color-permuting twists.