176 citations · 1.3k across the 156 of their papers we have counts for
11 papers · 1 filter
The L-Move and Virtual Braids
Louis H. Kauffman, Sofia Lambropoulou
This paper is a short introduction to and statement of the main theorems of our paper "Virtual Braids and the L-Move", JKTR, Vol. 15, No. 6 (2006), pp. 773-811. See also arxiv:Math…
Virtual Homotopy
H. A. Dye, Louis H. Kauffman
Two welded (respectively virtual) link diagrams are homotopic if one may be transformed into the other by a sequence of extended Reidemeister moves, classical Reidemeister moves, a…
Virtual Extension of Temperley--Lieb Algebra
Yong Zhang, Louis H. Kauffman, Mo-Lin Ge
The virtual knot theory is a new interesting subject in the recent study of low dimensional topology. In this paper, we explore the algebraic structure underlying the virtual braid…
Quantum Hidden Subgroup Algorithms: An Algorithmic Toolkit
Samuel J. Lomonaco, Louis H. Kauffman
One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev.…
- Deformed Spin Networks, Knot Polynomials and Anyonic Topological Quantum Computation
Louis H. Kauffman, Samuel J. Lomonaco
We review the q-deformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in…
Permutation and Its Partial Transpose
Yong Zhang, Louis H. Kauffman, Reinhard F. Werner
Permutation and its partial transpose play important roles in quantum information theory. The Werner state is recognized as a rational solution of the Yang--Baxter equation, and th…