Quantum computing thanks to Bianchi groups
Université de Bourgogne/Franche Comté, Institut FEMTO-ST UMR 6174, 15 B Avenue des Montboucons, F-25044 Besançon, France
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Published online: 15 January 2019
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 non-stabilizer eigenstates of permutation gates with the Pauli group acting on it . Further work observed that most found low-dimensional MICs may be built from subgroups of the modular group PS L(2, Z)  and that this can be understood from the picture of the trefoil knot and related 3-manifolds . Here one concentrates on Bianchi groups PS L(2, O10) (with O10 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 .
© The Authors, published by EDP Sciences, 2019
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