  A scheme is proposed for protecting quantum states from both independent
decoherence and cooperative decoherence. The scheme operates by pairing each
qubit (two-state quantum system) with an ancilla qubit and by encoding the
states of the qubits into the corresponding coherence-preserving states of the
qubit-pairs. In this scheme, the amplitude damping (loss of energy) is
prevented as well as the phase damping (dephasing) by a strategy called the
free-Hamiltonian-elimination We further extend the scheme to include quantum
gate operations and show that loss and decoherence during the gate operations
can also be prevented.
