  We analyze simple quantum error detection and quantum error correction
protocols relevant to current experiments with superconducting qubits. We show
that for qubits with energy relaxation the repetitive N-qubit codes cannot be
used for quantum error correction, but can be used for quantum error detection.
In the latter case it is sufficient to use only two qubits for the encoding. In
the analysis we demonstrate a useful technique of unraveling the qubit energy
relaxation into "relaxation" and "no relaxation" scenarios. Also, we propose
and numerically analyze several two-qubit algorithms for quantum error
detection/correction, which can be readily realized at the present-day level of
the phase qubit technology.
