Possible topological quantum computation via Khovanov homology: D-brane topological quantum computer

Mario Vélez; Juan Ospina

doi:10.1117/12.818551

27 April 2009 Possible topological quantum computation via Khovanov homology: D-brane topological quantum computer

Mario Vélez, Juan Ospina

Proceedings Volume 7342, Quantum Information and Computation VII; 73420P (2009) https://doi.org/10.1117/12.818551
Event: SPIE Defense, Security, and Sensing, 2009, Orlando, Florida, United States

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.

Citation Download Citation

Mario Vélez and Juan Ospina "Possible topological quantum computation via Khovanov homology: D-brane topological quantum computer", Proc. SPIE 7342, Quantum Information and Computation VII, 73420P (27 April 2009); https://doi.org/10.1117/12.818551

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