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Communication Dans Un Congrès Année : 2019

Quantum computing with Bianchi groups

Raymond Aschheim
Marcelo Amaral
Klee Irwin

Résumé

It has been shown that non-stabilizer eigenstates of permutation gates are appropriate for allowing $d$-dimensional universal quantum computing (uqc) based on minimal informationally complete POVMs. The relevant quantum gates may be built from subgroups of finite index of the modular group $\Gamma=PSL(2,\mathbb{Z})$ [M. Planat, Entropy 20, 16 (2018)] or more generally from subgroups of fundamental groups of $3$-manifolds [M. Planat, R. Aschheim, M.~M. Amaral and K. Irwin, arXiv 1802.04196(quant-ph)]. In this paper, previous work is encompassed by the use of torsion-free subgroups of Bianchi groups for deriving the quantum gate generators of uqc. A special role is played by a chain of Bianchi congruence $n$-cusped links starting with Thurston's link.

Dates et versions

hal-02290749 , version 1 (17-09-2019)

Identifiants

Citer

Michel Planat, Raymond Aschheim, Marcelo Amaral, Klee Irwin. Quantum computing with Bianchi groups. Quantum Technology International Conference 2018, Sep 2018, Paris, France. pp.0012, ⟨10.1051/epjconf/201919800012⟩. ⟨hal-02290749⟩
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