Generalized Cluster States Based on Finite Groups

TL;DR

This paper introduces a new class of generalized cluster states based on finite group algebras, extending the concept of cluster states and exploring their properties and potential applications.

Contribution

It establishes a correspondence between CSS-structured systems and finite group algebras, generalizing cluster states and analyzing their properties and connections to quantum double models.

Findings

Derived PEPS representations of the generalized states

Identified global symmetries of the states

Explored relationships to Kitaev quantum double models

Abstract

We define generalized cluster states based on finite group algebras in analogy to the generalization of the toric code to the Kitaev quantum double models. We do this by showing a general correspondence between systems with CSS structure and finite group algebras, and applying this to the cluster states to derive their generalization. We then investigate properties of these states including their PEPS representations, global symmetries, and relationship to the Kitaev quantum double models. We also discuss possible applications of these states.