High-threshold universal quantum computation on the surface code

We present a comprehensive and self-contained simplified review of the quantum computing scheme of Raussendorf [Phys. Rev. Lett. 98, 190504 (2007); N. J. Phys. 9, 199 (2007)], which features a two-dimensional nearest-neighbor coupled lattice of qubits, a threshold error rate approaching 1%, natural asymmetric and adjustable strength error correction, and low overhead arbitrarily long-range logical gates. These features make it one of the best and most practical quantum computing schemes devised to date. We restrict the discussion to direct manipulation of the surface code using the stabilizer formalism, both of which we also briefly review, to make the scheme accessible to a broad audience.