TY - CHAP

T1 - Monodromy analysis of the computational power of the Ising topological quantum computer

AU - Ahlbrecht, Andre

AU - Georgiev, Lachezar S.

AU - Werner, Reinhard F.

PY - 2010

Y1 - 2010

N2 - 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 $n$ 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.

AB - 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 $n$ 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.

U2 - 10.1063/1.3460174

DO - 10.1063/1.3460174

M3 - Beitrag in Buch/Sammelwerk

VL - 1243

T3 - AIP Conference Proceedings

SP - 279

EP - 288

BT - Lie theory and its applications in physics

A2 - Dobrev, V

ER -