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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Notes
It is also known as “logical" basis.
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Acknowledgements
The authors would like to express their extreme gratitude to the Illinois Geometry Lab at the University of Illinois at Urbana-Champaign, from which this work originated. R. Araiza and P. Wu would like to thank Thomas Sinclair for comments on an earlier draft of the manuscript. R. Araiza was funded as a JL Doob Research Assistant Professor during the writing of this manuscript.
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Araiza, R., Cai, J., Chen, Y. et al. A note on the stabilizer formalism via noncommutative graphs. Quantum Inf Process 23, 84 (2024). https://doi.org/10.1007/s11128-024-04291-3
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DOI: https://doi.org/10.1007/s11128-024-04291-3