General Scheme for the Construction of a Protected Qubit Subspace

We present a new robust decoupling scheme suitable for levels with either half-integer or integer angular momentum states. Through continuous dynamical decoupling techniques, we create a protected qubit subspace, utilizing a multistate qubit construction. Remarkably, the multistate system can also be composed of multiple substates within a single level. Our scheme can be realized with state-of-the-art experimental setups and thus has immediate applications for quantum information science. While the scheme is general and relevant for a multitude of solid-state and atomic systems, we analyze its performance for the case composed of trapped ions. Explicitly, we show how single qubit gates and an ensemble coupling to a cavity mode can be implemented efficiently. The scheme predicts a coherence time of ∼1 s, as compared to typically a few milliseconds for the bare states.