Quantum algorithms for the Jones polynomial and Khovanov homology
Louis Hirsch Kauffman, Samuel J. Lomonaco · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2012
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.