Noise Threshold for a Fault-Tolerant Two-Dimensional Lattice Architecture

Details Noise Threshold for a Fault-Tolerant Two-Dimensional Lattice Architecture Noise Threshold for a Fault-Tolerant Two-Dimensional Lattice Architecture

2006-04-12

arxiv.org/abs/quant-ph/0604090v3

Quant. Inf. Comp. Vol. 7, No. 4, pp. 297-318 (2007)

Physics

Quantum Physics

20 pages, 11 figures. v2 has some small changes and a link to a website with supplementary material. v3: Corrects earlier erro

Scientific paper

We consider a model of quantum computation in which the set of operations is limited to nearest-neighbor interactions on a 2D lattice. We model movement of qubits with noisy SWAP operations. For this architecture we design a fault-tolerant coding scheme using the concatenated [[7,1,3]] Steane code. Our scheme is potentially applicable to ion-trap and solid-state quantum technologies. We calculate a lower bound on the noise threshold for our local model using a detailed failure probability analysis. We obtain a threshold of 1.85 x 10^-5 for the local setting, where memory error rates are one-tenth of the failure rates of gates, measurement, and preparation steps. For the analogous nonlocal setting, we obtain a noise threshold of 3.61 x 10^-5. Our results thus show that the additional SWAP operations required to move qubits in the local model affect the noise threshold only moderately.

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