  We study various aspects of the topological quantum computation scheme based
on the non-Abelian anyons corresponding to fractional quantum hall effect
states at filling fraction 5/2 using the Temperley-Lieb recoupling theory.
Unitary braiding matrices are obtained by a normalization of the degenerate
ground states of a system of anyons, which is equivalent to a modification of
the definition of the 3-vertices in the Temperley-Lieb recoupling theory as
proposed by Kauffman and Lomonaco. With the braid matrices available, we
discuss the problems of encoding of qubit states and construction of quantum
gates from the elementary braiding operation matrices for the Ising anyons
model. In the encoding scheme where 2 qubits are represented by 8 Ising anyons,
we give an alternative proof of the no-entanglement theorem given by Bravyi and
compare it to the case of Fibonacci anyons model. In the encoding scheme where
2 qubits are represented by 6 Ising anyons, we construct a set of quantum gates
which is equivalent to the construction of Georgiev.
