Previous Article in Journal
Quantum Blockchain Using Entanglement in Time
Article Menu

Export Article

Open AccessArticle

Quantum Computing, Seifert Surfaces, and Singular Fibers

1
Institut FEMTO-ST CNRS UMR 6174, Université de Bourgogne/Franche-Comté, 15 B Avenue des Montboucons, F-25044 Besançon, France
2
Quantum Gravity Research, Los Angeles, CA 90290, USA
*
Author to whom correspondence should be addressed.
Quantum Reports 2019, 1(1), 12-22; https://doi.org/10.3390/quantum1010003
Received: 11 March 2019 / Revised: 3 April 2019 / Accepted: 17 April 2019 / Published: 24 April 2019
  |  
PDF [1006 KB, uploaded 29 April 2019]
  |     |  

Abstract

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
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Planat, M.; Aschheim, R.; Amaral, M.M.; Irwin, K. Quantum Computing, Seifert Surfaces, and Singular Fibers. Quantum Reports 2019, 1, 12-22.

Show more citation formats Show less citations formats

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Quantum Reports EISSN 2624-960X Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top