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Communication Dans Un Congrès Année : 2018

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].
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hal-02867890 , version 1 (15-06-2020)

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Michel Planat. Quantum computing thanks to Bianchi groups. Quantum Technology International Conference, Sep 2018, Paris, France. ⟨hal-02867890⟩
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