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We give a general proof for the existence and realizability of Clifford gatesin the Ising topological quantum computer. We show that all quantum gates thatcan be implemented by braiding of Ising anyons are Clifford gates. We find thatthe braiding gates for two qubits exhaust the entire two-qubit Clifford group.Analyzing the structure of the Clifford group for n \geq 3 qubits we prove thatthe the image of the braid group is a non-trivial subgroup of the Cliffordgroup so that not all Clifford gates could be implemented by braiding in theIsing topological quantum computation scheme. We also point out which Cliffordgates cannot in general be realized by braiding.

Implementation of Clifford gates in the Ising-anyon topological quantum computer