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Article Dans Une Revue Quantum Rep. Année : 2019

Quantum computing, Seifert surfaces and singular fibers

Résumé

The fundamental group π 1 ( L ) of a knot or link L may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete information about the processed quantum states. In this paper, one defines braids whose closure is the L of such a quantum computer model and computes their braid-induced Seifert surfaces and the corresponding Alexander polynomial. In particular, some d-fold coverings of the trefoil knot, with d = 3 , 4, 6, or 12, define appropriate links L, and the latter two cases connect to the Dynkin diagrams of E 6 and D 4 , respectively. In this new context, one finds that this correspondence continues with Kodaira’s classification of elliptic singular fibers. The Seifert fibered toroidal manifold Σ ′ , at the boundary of the singular fiber E 8 ˜ , allows possible models of quantum computing.

Dates et versions

hal-02290823 , version 1 (18-09-2019)

Identifiants

Citer

Michel Planat, Raymond Aschheim, Marcelo M. Amaral, Klee Irwin. Quantum computing, Seifert surfaces and singular fibers. Quantum Rep., 2019, 1 (1), pp.12-22. ⟨10.3390/quantum1010003⟩. ⟨hal-02290823⟩
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