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Proceedings Paper

Possible topological quantum computation via Khovanov homology: D-brane topological quantum computer
Author(s): Mario Vélez; Juan Ospina
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Paper Abstract

A model of a D-Brane Topological Quantum Computer (DBTQC) is presented and sustained. The model is based on four-dimensional TQFTs of the Donaldson-Witten and Seiber-Witten kinds. It is argued that the DBTQC is able to compute Khovanov homology for knots, links and graphs. The DBTQC physically incorporates the mathematical process of categorification according to which the invariant polynomials for knots, links and graphs such as Jones, HOMFLY, Tutte and Bollobás-Riordan polynomials can be computed as the Euler characteristics corresponding to special homology complexes associated with knots, links and graphs. The DBTQC is conjectured as a powerful universal quantum computer in the sense that the DBTQC computes Khovanov homology which is considered like powerful that the Jones polynomial.

Paper Details

Date Published: 27 April 2009
PDF: 12 pages
Proc. SPIE 7342, Quantum Information and Computation VII, 73420P (27 April 2009); doi: 10.1117/12.818551
Show Author Affiliations
Mario Vélez, EAFIT Univ. (Colombia)
Juan Ospina, EAFIT Univ. (Colombia)

Published in SPIE Proceedings Vol. 7342:
Quantum Information and Computation VII
Eric J. Donkor; Andrew R. Pirich; Howard E. Brandt, Editor(s)

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