  The unitary braiding operators describing topological entanglements can be
viewed as universal quantum gates for quantum computation. With the help of the
Brylinskis'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 braided 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 Schr{\"o}dinger equations.
