176 citations · 1.3k across the 156 of their papers we have counts for
8 papers · 1 filter
An Extended Bracket Polynomial for Virtual Knots and Links
Louis H. Kauffman
This paper defines a new invariant of virtual knots and links that we call the extended bracket polynomial, and denote by <<K>> for a virtual knot or link K. This invariant is a st…
Determinants of rational knots
Louis H. Kauffman, Pedro Lopes
We study the Fox coloring invariants of rational knots. We express the propagation of the colors down the twists of these knots and ultimately the determinant of them with the help…
A State Sum Link Invariant of Regular Isotopy
Louis H. Kauffman, Simon King, Sostenes Lins
This paper has been withdrawn because there is a fundamental error in the computations; with the right computational scheme it seems to be just a version of the Jones polynomial
Spin Networks and Anyonic Topological Computing II
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…
A 3-Stranded Quantum Algorithm for the Jones Polynomial
Louis H. Kauffman, Samuel J. Lomonaco
Let K be a 3-stranded knot (or link), and let L denote the number of crossings in K. Let and be two positive real numbers such that is less than or equal to…
Topological-Like Features in Diagrammatical Quantum Circuits
Yong Zhang, Louis H. Kauffman
In this paper, we revisit topological-like features in the extended Temperley--Lieb diagrammatical representation for quantum circuits including the teleportation, dense coding and…