Condensed Encodings of Projective Clifford Operations in Arbitrary Dimension

TL;DR

This paper analyzes the structure of the n-qudit projective Clifford group across all dimensions, providing formulas for evaluation, composition, and inversion, with special emphasis on the even dimension case.

Contribution

It introduces new formulas for key operations in the projective Clifford group applicable to all dimensions, including even ones, enhancing understanding and manipulation of these groups.

Findings

Derived formulas for evaluation, composition, and inversion of Clifford elements

Unified treatment of the Clifford group structure for all dimensions

Special focus on the even dimension case

Abstract

We provide a careful analysis of the structure theorem for the $n$-qudit projective Clifford group and various encoding schemes for its elements. In particular, we derive formulas for evaluation, composition, and inversion. Our results apply to all integers $d\geq2$, most notably the even case.