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

• Received 24 March 1997

DOI:https://doi.org/10.1103/PhysRevLett.79.1953