25 citations · 125 across the 36 of their papers we have counts for
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quant-ph2009
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.,…
quant-ph2009★ 1 cited
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.
math.GT2009
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…