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Quantum Information Processing

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01-03-2024

A note on the stabilizer formalism via noncommutative graphs

Authors: Roy Araiza, Jihong Cai, Yushan Chen, Abraham Holtermann, Chieh Hsu, Tushar Mohan, Peixue Wu, Zeyuan Yu

Published in: Quantum Information Processing | Issue 3/2024

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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 finite groups and suitably chosen operators on finite-dimensional Hilbert spaces. This type of construction exhibits all the correctable errors by the stabilizer codes. Furthermore, in this framework, we generalize previous results in this area for determining when such noncommutative graphs have anticliques.

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It is also known as “logical" basis.

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Title: A note on the stabilizer formalism via noncommutative graphs
Authors: Roy Araiza
Jihong Cai
Yushan Chen
Abraham Holtermann
Chieh Hsu
Tushar Mohan
Peixue Wu
Zeyuan Yu
Publication date: 01-03-2024
Publisher: Springer US
Published in: Quantum Information Processing / Issue 3/2024
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-024-04291-3

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