Effect of ancilla’s structure on quantum error correction using the seven-qubit Calderbank-Shor-Steane code
Pedro J. Salas, Angel L. Sanz · Physical Review A · 2004
In this work we discuss the ability of different types of ancillas to control the decoherence of a qubit interacting with an environment. The error is introduced into the numerical simulation via a depolarizing isotropic channel. The ranges of values considered are ${10}^{\ensuremath{-}4}\ensuremath{\leqslant}\ensuremath{\epsilon}\ensuremath{\leqslant}{10}^{\ensuremath{-}2}$ for memory errors and $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\ensuremath{\leqslant}\ensuremath{\gamma}∕7\ensuremath{\leqslant}{10}^{\ensuremath{-}2}$ for gate errors. After the correction we calculate the fidelity as a quality criterion for the qubit recovered. We observe that a recovery method with a three-qubit ancilla provides reasonably good results bearing in mind its economy. If we want to go further, we have to use fault tolerant ancillas with a high degree of parallelism, even if this condition implies introducing additional ancilla verification qubits.