Condensed Matter Seminar: Analytical and Numerical results for the Fidelity of the Surface Code

The surface code is a promising alternative for implementing fault-tolerant, large-scale quantum information processing. Its high threshold for single-qubit errors under stochastic noise is one of its most attractive features. We develop an exact formulation for the fidelity of the surface code that allows us to probe much further on this promise of strong protection. This formulation goes beyond the stochastic single-qubit error model approximation and can take into account both correlated errors and inhomogeneities in the coupling between physical qubits and the environment. Exact results for the fidelity threshold of the surface code are obtained for several relevant types of noise. Analytical predictions for a representative case are confirmed by Monte Carlo simulations.