A note on the stabilizer formalism via noncommutative graphs

TL;DR

This paper reformulates the stabilizer formalism using noncommutative graphs derived from unitary group representations, providing a generalized framework for identifying anticliques in quantum graph structures.

Contribution

It introduces a novel formulation of the stabilizer formalism through noncommutative graphs based on unitary representations, extending previous results in quantum graph theory.

Findings

Generalized conditions for anticliques in noncommutative graphs

Unified framework linking stabilizer formalism and noncommutative graphs

Extension of prior results to broader classes of quantum graphs

Abstract

In this short note we formulate a stabilizer formalism in the language of noncommutative graphs. The classes of noncommutative graphs we consider are obtained via unitary representations of compact groups, and suitably chosen operators on finite-dimensional Hilbert spaces. Furthermore, in this framework, we generalize previous results in this area for determining when such noncommutative graphs have anticliques.