Clifford operators in SU(N)1; N not odd prime

TL;DR

This paper discusses the construction of Clifford operators for qudits of any dimension, showing they can be derived from operations in SU(N)1, and explores a witness for W3 states in SU(2)1.

Contribution

It demonstrates that Clifford operators for all qudit dimensions can be constructed from SU(N)1 operations, extending previous characterizations to even and odd dimensions.

Findings

Clifford operators are obtainable from SU(N)1 operations for all N.

A witness for W3 states in SU(2)1 is discussed.

The approach unifies the construction of Clifford gates across different dimensions.

Abstract

Farinholt gives a characterization of Clifford operators for qudits; d both odd and even. In this comment it is shown that the necessary gates for the construction of Clifford operators; N both odd and even, are obtained directly from operations that appear in SU(N)1. A witness for W3 states in SU(2)1 is discussed. See e.g. [1-4].