Noise Threshold for a Fault-Tolerant Two-Dimensional Lattice Architecture
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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.
20 pages, 11 figures. v2 has some small changes and a link to a website with supplementary material. v3: Corrects earlier error in fault tolerant T gate construction. Describes different strategy for non-Clifford fault tolerance
20 pages, 11 figures. v2 has some small changes and a link to a website with supplementary material. v3: Corrects earlier error in fault tolerant T gate construction. Describes different strategy for non-Clifford fault tolerance