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Is quantum computing with superfluid helium possible: a potential role of Khovanov homology
by
Robert Owczarek
Enfitec, Inc.
Coauthors: L. H. Kauffman, J. H. Przytycki
Khovanov homology and related knot invariants open new ways for studying quantum statistical mechanics. One system of potential interest is superfluid helium. Namely, critical superfluid helium is a tangle of vortex loops, requiring description in terms of knot theory, which was never actually done, despite a number of attempts. My recent discussions with knot theorists showed some research directions that look promising. I am going to present a very preliminary discussion of the framework of the description of superfluid helium vortices in terms of Khovanov homology. I am also going to disuss shortly potential application of this system for quantum computing, in particular of the issue of which natural unitary operators are describing genuine quantum processes.
Date received: March 21, 2011
Copyright © 2011 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbcc-04.