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Quantum Computing, Seifert Surfaces, and Singular Fibers

Institut FEMTO-ST CNRS UMR 6174, Université de Bourgogne/Franche-Comté, 15 B Avenue des Montboucons, F-25044 Besançon, France
Quantum Gravity Research, Los Angeles, CA 90290, USA
Author to whom correspondence should be addressed.
Quantum Reports 2019, 1(1), 12-22;
Received: 11 March 2019 / Revised: 3 April 2019 / Accepted: 17 April 2019 / Published: 24 April 2019
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. View Full-Text
Keywords: quantum computing; Seifert surfaces; singular fibers quantum computing; Seifert surfaces; singular fibers
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Planat, M.; Aschheim, R.; Amaral, M.M.; Irwin, K. Quantum Computing, Seifert Surfaces, and Singular Fibers. Quantum Reports 2019, 1, 12-22.

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