Probabilities of failure for quantum error correction
Scott, A J · CERN Document Server (European Organization for Nuclear Research) · 2004
We investigate the integrity of a quantum error-correcting code when pushed beyond its intended capacity, presenting formulae for the probability of failure when the errors affect more qudits than that specified by the code's minimum distance. We consider both error detection and error correction. Explicit examples are treated in the case of stabilizer codes constructed from qubits and encoding a single qubit.