  We show that all quantum gates which could be implemented by braiding of
Ising anyons in the Ising topological quantum computer preserve the n-qubit
Pauli group. Analyzing the structure of the Pauli group's centralizer, also
known as the Clifford group, for n\geq 3 qubits, we prove that the image of the
braid group is a non-trivial subgroup of the Clifford group and therefore not
all Clifford gates could be implemented by braiding. We show explicitly the
Clifford gates which cannot be realized by braiding estimating in this way the
ultimate computational power of the Ising topological quantum computer.
