176 citations · 1.3k across the 156 of their papers we have counts for
6 papers · 2 filters
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…
Topological Quantum Computing and the Jones Polynomial
Samuel J. Lomonaco, Louis H. Kauffman
In this paper, we give a description of a recent quantum algorithm created by Aharonov, Jones, and Landau for approximating the values of the Jones polynomial at roots of unity of…
Spin Networks and Anyonic Topological Computing
Louis H. Kauffman, Samuel J. Lomonaco
We review the q-deformed spin network approact to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in…
Is Grover's Algorithm a Quantum Hidden Subgroup Algorithm ?
Samuel J. Lomonaco, Louis H. Kauffman
The arguments given in this paper suggest that Grover's and Shor's algorithms are more closely related than one might at first expect. Specifically, we show that Grover's algorithm…