Multimode superconducting qubit with three-wave mixing interaction for dual-rail encoding

We present a novel multi-mode qubit for hardware efficient dual-rail encoding. The qubit includes a three-wave mixing element which provides the necessary interaction for side-band transitions between modes while still being at a quadratically insensitive bias point. We show this is due to the inherent protection of the logical encoding from flux noise. One of these transitions realizes a single-qubit gate of the dual-rail qubit without leaving the logical single-excitation subspace and therefore provides additional protection from bit-flip errors. Wide tunability and the richness of interactions enables a variety of two-qubit gates for coupled dual-rail qubits.