Fault-tolerant quantum computation with local gates
Abstract
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.
- Publication:
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Journal of Modern Optics
- Pub Date:
- February 2000
- DOI:
- 10.1080/09500340008244046
- arXiv:
- arXiv:quant-ph/9903099
- Bibcode:
- 2000JMOp...47..333G
- Keywords:
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- Quantum Physics
- E-Print:
- 14 pages, LaTeX