Active suppression of dephasing in Josephson-junction qubits

Simple majority code correcting $k$ dephasing errors by encoding a qubit of information into $2k+1$ physical qubits is studied quantitatively. We derive an equation for quasicontinuous evolution of the density matrix of encoded quantum information under the error correction procedure in the presence of correlated dephasing noise. A specific design of a Josephson-junction nanocircuit implementing this scheme is suggested.