Quantum Information Processing, Vol. 4, No. 3, August 2005 (© 2005)
Yang–Baxterizations, Universal Quantum Gates
Louis H. Kauffman,
and Mo-Lin Ge
Received March 11, 2005; accepted June 17, 2005
The unitary braiding operators describing topological entanglements can be viewed as
universal quantum gates for quantum computation. With the help of the Brylinski’s the-
orem, the unitary solutions of the quantum Yang–Baxter equation can be also related
to universal quantum gates. This paper derives the unitary solutions of the quantum
Yang–Baxter equation via Yang–Baxterization from the solutions of the braid rela-
tion. We study Yang–Baxterizations of the non-standard and standard representations
of the six-vertex model and the complete solutions of the non-vanishing eight-vertex
model. We construct Hamiltonians responsible for the time-evolution of the unitary
braiding operators which lead to the Schr
KEY WORDS: Topological entanglement; quantum entanglement; braid group
representation; quantum Yang–Baxter equation.
PACS NUMBERS: 02.10.Kn, 03.65.Ud, 03.67.Lx
There are natural relationships between quantum entanglement
Topology studies global relationships in
spaces, and how one space can be placed within another, such as knot-
ting and linking of curves in three-dimensional space. One way to study
topological entanglement and quantum entanglement is to try making
Institute of Theoretical Physics, Chinese Academy of Sciences, P. O. Box 2735, Beijing
100080, P. R. China.
Department of Mathematics, Statistics and Computer Science, University of Illinois at
Chicago, 851 South Morgan Street, Chicago, IL, 60607-7045, USA.
Nankai Institute of Mathematics, Nankai University, Tianjin 300071, P. R. China.
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1570-0755/05/0800-0159/0 © 2005 Springer Science+Business Media, Inc.