Quantum Error Correction on Linear Nearest Neighbor Qubit Arrays

A minimal depth quantum circuit implementing 5-qubit quantum error correction in a manner optimized for a linear nearest neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that incorporate the necessary swap operations. Simulations of the circuit's performance when subjected to discrete and continuous errors are presented. The relationship between the error rate of a physical qubit and that of a logical qubit is investigated with emphasis on determining the concatenated error correction threshold.