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Article Dans Une Revue Symmetry Année : 2018

Universal quantum computing and three-manifolds

Raymond Aschheim
Marcelo M. Amaral
  • Fonction : Auteur
Klee Irwin

Résumé

A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S 3 . Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-valued measure (POVM) that one recognizes to be a 3-manifold M 3 . More precisely, the d-dimensional POVMs defined from subgroups of finite index of the modular group P S L ( 2 , Z ) correspond to d-fold M 3 - coverings over the trefoil knot. In this paper, we also investigate quantum information on a few ‘universal’ knots and links such as the figure-of-eight knot, the Whitehead link and Borromean rings, making use of the catalog of platonic manifolds available on the software SnapPy. Further connections between POVMs based UQC and M 3 ’s obtained from Dehn fillings are explored.

Dates et versions

hal-01867267 , version 1 (04-09-2018)

Identifiants

Citer

Michel Planat, Raymond Aschheim, Marcelo M. Amaral, Klee Irwin. Universal quantum computing and three-manifolds. Symmetry, 2018, 10 (12), pp.773. ⟨10.3390/sym10120773⟩. ⟨hal-01867267⟩
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