Fault-Tolerant Quantum Computation with Local Gates

Details Fault-Tolerant Quantum Computation with Local Gates Fault-Tolerant Quantum Computation with Local Gates

1999-03-30

arxiv.org/abs/quant-ph/9903099v1

J.Mod.Opt. 47 (2000) 333-345

Physics

Quantum Physics

14 pages, LaTeX

Scientific paper

I discuss how to perform fault-tolerant quantum computation with concatenated codes using local gates in small numbers of dimensions. I show that a threshold result still exists in three, two, or one dimensions when next-to-nearest-neighbor gates are available, and present explicit constructions. In two or three dimensions, I also show how nearest-neighbor gates can give a threshold result. In all cases, I simply demonstrate that a threshold exists, and do not attempt to optimize the error correction circuit or determine the exact value of the threshold. The additional overhead due to the fault-tolerance in both space and time is polylogarithmic in the error rate per logical gate.

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