Abstract Error Groups Via Jones Unitary Braid Group Representations at q=i - Quantum PhysicsReport as inadecuate




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Abstract: In this paper, we classify a type of abstract groups by the central productsof dihedral groups and quaternion groups. We recognize them as abstract errorgroups which are often not isomorphic to the Pauli groups in the literature. Weshow the corresponding nice error bases equivalent to the Pauli error basesmodulo phase factors. The extension of these abstract groups by the symmetricgroup are finite images of the Jones unitary representations or modulo a phasefactor of the braid group at q=i or r=4. We hope this work can finally lead tonew families of quantum error correction codes via the representation theory ofthe braid group.



Author: Yong Zhang UCF

Source: https://arxiv.org/







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