Topological-Like Features in Diagrammatical Quantum Circuits

Authors:
Yong Zhang;Louis H. Kauffman
Affiliations:
Department of Physics, University of Utah, Salt Lake City, USA 84112-0830;Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, USA 60607-7045
Venue:
Quantum Information Processing
Year:
2008

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Abstract

In this paper, we revisit topological-like features in the extended Temperley---Lieb diagrammatical representation for quantum circuits including the teleportation, dense coding and entanglement swapping. We describe these quantum circuits and derive characteristic equations for them with the help of topological-like operations. Furthermore, we comment on known diagrammatical approaches to quantum information phenomena from the perspectives of both tensor categories and topological quantum field theories. Moreover, we remark on the proposal for categorical quantum physics and information as described by dagger ribbon categories.