Local Fault-tolerant Quantum Computation

Details Local Fault-tolerant Quantum Computation Local Fault-tolerant Quantum Computation

2004-10-06

arxiv.org/abs/quant-ph/0410047v2

Phys. Rev. A 72, 022317 (2005) (17 pages)

Physics

Quantum Physics

REVTeX, 44 pages, 19 figures, to appear in Physical Review A

Scientific paper

10.1103/PhysRevA.72.022317

We analyze and study the effects of locality on the fault-tolerance threshold for quantum computation. We analytically estimate how the threshold will depend on a scale parameter r which estimates the scale-up in the size of the circuit due to encoding. We carry out a detailed semi-numerical threshold analysis for concatenated coding using the 7-qubit CSS code in the local and `nonlocal' setting. First, we find that the threshold in the local model for the [[7,1,3]] code has a 1/r dependence, which is in correspondence with our analytical estimate. Second, the threshold, beyond the 1/r dependence, does not depend too strongly on the noise levels for transporting qubits. Beyond these results, we find that it is important to look at more than one level of concatenation in order to estimate the threshold and that it may be beneficial in certain places, like in the transportation of qubits, to do error correction only infrequently.

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