176 citations · 1.3k across the 156 of their papers we have counts for
7 papers · 1 filter
Quantum Knots and Lattices, or a Blueprint for Quantum Systems that Do Rope Tricks
Samuel J. Lomonaco, Louis H. Kauffman
Using the cubic honeycomb (cubic tessellation) of Euclidean 3-space, we define a quantum system whose states, called quantum knots, represent a closed knotted piece of rope, i.e.,…
Anyonic Topological Quantum Computation and the Virtual Braid Group
H. A. Dye, Louis H. Kauffman
We introduce a recoupling theory for virtual braided trees. This recoupling theory can be utilized to incorporate swap gates into anyonic models of quantum computation.
NMR Quantum Calculations of the Jones Polynomial
Raimund Marx, Amr Fahmy, Louis Kauffman +5
The repertoire of problems theoretically solvable by a quantum computer recently expanded to include the approximate evaluation of knot invariants, specifically the Jones polynomia…
Remarks on Khovanov Homology and the Potts Model
Louis H. Kauffman
This paper is dedicated to Oleg Viro on his 60-th birthday. The paper is about Khovanov homology and its relationships with statistical mechanics models such as the Ising model and…
On two categorifications of the arrow polynomial for virtual knots
Heather Ann Dye, Louis Hirsch Kauffman, Vassily Olegovich Manturov
Two categorifications are given for the arrow polynomial, an extension of the Kauffman bracket polynomial for virtual knots. The arrow polynomial extends the bracket polynomial to…
Lower bounds on virtual crossing number and minimal surface genus
Kumud Bhandari, H. A. Dye, Louis H. Kauffman
We compute lower bounds on the virtual crossing number and minimal surface genus of virtual knot diagrams from the arrow polynomial. In particular, we focus on several interesting…