Monodromy analysis of the computational power of the Ising topological quantum computer

Details Monodromy analysis of the computational power of the Ising topological quantum computer Monodromy analysis of the computational power of the Ising topological quantum computer

2009-11-13

arxiv.org/abs/0911.2591v2

Physics

Mathematical Physics

10 pages, 2 figures and 1 table; v2: one more reference added and some typos corrected; Talk given at the VIII International W

Scientific paper

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.

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