Quantum Knots and Quantum Braids

Dr. Samuel J. Lomonaco
University of Maryland, Baltimore County

Noon-1:00pm Friday, March 9, 2012, MP 401

In this talk, we show how to reconstruct knot theory in such a way that it s intimately related to quantum physics. In particular, we give a blueprint for creating a quantum system that has the dynamic behavior of a closed knotted piece of rope moving in 3-space. Within this framework, knot invariants become physically measurable quantum observables, knot moves become unitary transformations, with knot dynamics determined by Schroedinger's equation. The same approach can also be applied to the theory of braids. Toward the end of the talk, we briefly look at possible applications to superfluid vortices and to topological quantum computing in optical lattices.

Professor Lomonaco received his PhD in Mathematics from Princeton University. He has been a full professor of Computer Science and Electrical Engineering at the University of Maryland Baltimore County (UMBC) since 1985, serving as Founding Chair of the CS Department 1985 to 1991. Representative Awards, Accomplishments, and Honors inlcude the following.

• Professor Lomonaco is a member of the European Academy of Sciences.
• Visiting Key Research Scientist at the Mathematical Sciences Research Institute (MSRI) at the University of California at Berkley in 2004.
• Senior LaGrange Fellow at the Institute for Scientific Exchange in Torino, Italy in 2005.
• For contributions made to the development of the programming language Ada, he received an award from the United States Under Secretary of Defense for Research and Engineering, Dr. Richard DeLauer.
• First to introduce Quantum Information Science to the American Mathematical Society (AMS) by organizing and giving a two day AMS Short Course on Quantum Computation at the Annual Meeting of the AMS in Washington, DC in January 2000.
• He has published four books on Quantum Computation and Information Science, and one on Topology.
• He serves as associate editor of the Journal of Knot Theory
• He has currently accepted an invitation to be a guest editor of the Journal of Quantum Information Processing for a Special Issue on Topological Quantum Computation.