Title
Abstract Error Groups Via Jones Unitary Braid Group Representations At Q = I
Keywords
Abstract error group; Extra special two-groups; Nice error base; Unitary braid representation
Abstract
In this paper, we classify a type of abstract groups by the central products of dihedral groups and quaternion groups. We recognize them as abstract error groups which are often not isomorphic to the Pauli groups in the literature. We show the corresponding nice error bases equivalent to the Pauli error bases modulo phase factors. The extension of these abstract groups by the symmetric group are finite images of the Jones unitary representations (or modulo a phase factor) of the braid group at q = i or r = 4. We hope this work can finally lead to new families of quantum error correction codes via the representation theory of the braid group. © 2009 Springer Science+Business Media, LLC.
Publication Date
2-1-2009
Publication Title
Quantum Information Processing
Volume
8
Issue
1
Number of Pages
25-36
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1007/s11128-008-0092-7
Copyright Status
Unknown
Socpus ID
59249096643 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/59249096643
STARS Citation
Zhang, Yong, "Abstract Error Groups Via Jones Unitary Braid Group Representations At Q = I" (2009). Scopus Export 2000s. 12245.
https://stars.library.ucf.edu/scopus2000/12245