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- Title
Yang–Baxterizations, Universal Quantum Gates and Hamiltonians.
- Authors
Yong Zhang; Kauffman, Louis H.; Mo-Lin Ge
- Abstract
The unitary braiding operators describing topological entanglements can be viewed as universal quantum gates for quantum computation. With the help of the Brylinski’s theorem, 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 relation. 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 Schrödinger equations.
- Subjects
UNITARY operators; YANG-Baxter equation; MATHEMATICAL physics; QUANTUM field theory; HAMILTONIAN operator; HAMILTONIAN systems; DIFFERENTIAL operators; QUANTUM theory
- Publication
Quantum Information Processing, 2005, Vol 4, Issue 3, p159
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-005-7655-7