Generalized cluster states based on finite groups

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 st...

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Bibliographic Details
Published in:New journal of physics 2015-02, Vol.17 (2), p.23029-20
Main Author: Brell, Courtney G
Format: Article
Language:English
Subjects:
Algebra
Analogies
Clusters
fault-tolerant quantum computation
Group theory
Mathematical analysis
measurement-based quantum computation
Physics
Representations
Symmetry
topological computation
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Summary: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 projected entangled pair state representations, global symmetries, and relationship to the Kitaev quantum double models. We also discuss possible applications of these states.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/17/2/023029