Quantum computing thanks to Bianchi groups
Résumé
It has been shown that the concept of a magic state (in universal quantum computing: uqc) and that of a minimal informationally complete
positive operator valued measure: MIC-POVMs (in quantum measurements) are in good agreement when such a magic state is selected in the set of nonstabilizer eigenstates of permutation gates with the Pauli group acting on it [1].
Further work observed that most found low-dimensional MICs may be built from subgroups of the modular group PS L(2, Z) [2] and that this can be understood from the picture of the trefoil knot and related 3-manifolds [3]. Here one concentrates on Bianchi groups PS L(2,Od) (with Od the integer ring over the imaginary quadratic field) whose torsion-free subgroups define the appropriate knots and links leading to MICs and the related uqc. One finds a chain of Bianchi congruence n-cusped links playing a significant role [4].
Fichier principal
b1168c75-4524-4ada-8415-960cda5f6c2c-author.pdf (420.27 Ko)
Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...