期刊
PHYSICAL REVIEW A
卷 79, 期 3, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.79.032311
关键词
anyons; group theory; Ising model; quantum gates
资金
- DFG
- BG-NCSR [F-1406, DO 02-257]
We give a general proof for the existence and realizability of Clifford gates in the Ising topological quantum computer. We show that all quantum gates that can be implemented by braiding of Ising anyons are Clifford gates. We find that the braiding gates for two qubits exhaust the entire two-qubit Clifford group. Analyzing the structure of the Clifford group for n >= 3 qubits we prove that the image of the braid group is a nontrivial subgroup of the Clifford group so that not all Clifford gates could be implemented by braiding in the Ising topological quantum computation scheme. We also point out which Clifford gates cannot in general be realized by braiding.
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