Efficient schemes for reducing imperfect collective decoherences

Information processing with quantum bits is used to solve classical intractable problems. A scheme is proposed that is efficient even when a pair of qubits undergoes imperfect collective decoherence. The quantum Zeno effect was used to reduce the leakage out of the encoding space generated by the imperfection. Phase errors in the encoded bits were reduced by the concatenation of the decoherence free subspace with a three qubit quantum error correcting code.