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Quantum Error Correction Fault Tolerance
Decomposition of Pauli groups via weak central products
arXiv
Authors: Andrea Rocchetto, Francesco G. Russo
Year
2019
Paper ID
14606
Status
Preprint
Abstract Read
~2 min
Abstract Words
107
Citations
N/A
Abstract
For any m ge 1 and odd prime power mathtt{q}=mathtt{p}m, for mathtt{q}=2, and for any n ge 1, we show a result of decomposition for Pauli groups mathcal{P}_{n,mathtt{q}} in terms of weak central products. This can be used to describe the underlying structure of Pauli groups on n qudits of dimension mathtt{q} and enables us to identify abelian subgroups of mathcal{P}_{n,mathtt{q}}. As a consequence of our main results, we show a similar factorisation for the so--called `lifted' Pauli groups, recently introduced by Gottesman and Kuperberg in the context of error-correcting codes in quantum information theory.
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- This paper contributes to the Quantum Error Correction & Fault Tolerance research area in the Quantum Articles archive.
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- For any m ge 1 and odd prime power mathttq=mathttp^m, for mathttq=2, and for any n ge 1, we show a result of decomposition for Pauli groups mathcalP_n,mathttq in terms of weak...
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