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Any residual coupling of a quantum computer to the environment results incomputational errors. Encoding quantum information in a so-calleddecoherence-free subspace provides means to avoid these errors. Despitetremendous progress in employing this technique to extend memory storage timesby orders of magnitude, computation within such subspaces has been scarce.Here, we demonstrate the realization of a universal set of quantum gates actingon decoherence-free ion qubits. We combine these gates to realize the firstcontrolled-NOT gate within a decoherence-free, scalable quantum computer.

Realization of Universal Ion Trap Quantum Computation with Decoherence Free Qubits