General scheme for the construction of a protected qubit subspace

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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 multi-state qubit construction. Remarkably, the multi-state system can also be comprised of multiple sub-states 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 second, as compared to typically a few milliseconds for the bare states.