Quantum algorithms for the Jones polynomial and Khovanov homology

Louis H. Kauffman; Samuel J. Lomonaco Jr.

doi:10.1117/12.918987

8 May 2012 Quantum algorithms for the Jones polynomial and Khovanov homology

Louis H. Kauffman, Samuel J. Lomonaco Jr.

Proceedings Volume 8400, Quantum Information and Computation X; 84000V (2012) https://doi.org/10.1117/12.918987
Event: SPIE Defense, Security, and Sensing, 2012, Baltimore, Maryland, United States

Abstract

This paper generalizes the AJL algorithm for quantum computation of the Jones polynomial to continuous ranges of values on the unit circle for the Jones parameter and shows that the Kauffman-Lomonaco 3-strand algorithm for the Jones polynomial is a special case of this generalization. We then describe a quantum algorithm for the Jones polynomial that is related to Khovanov homology.

Citation Download Citation

Louis H. Kauffman and Samuel J. Lomonaco Jr. "Quantum algorithms for the Jones polynomial and Khovanov homology", Proc. SPIE 8400, Quantum Information and Computation X, 84000V (8 May 2012); https://doi.org/10.1117/12.918987

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