Pokemon: Protected Logic Qubit Derived from the 0-$\pi$ Qubit

We propose a new protected logic qubit called pokemon, which is derived from the 0-$\pi$ qubit by harnessing one capacitively shunted inductor and two capacitively shunted Josephson junctions embedded in a superconducting loop. Similar to the 0-$\pi$ qubit, the two basis states of the proposed qubit are separated by a high barrier, but their wave functions are highly localized along both axis directions of the two-dimensional parameter space, instead of the highly localized wave functions along only one axis direction in the 0-$\pi$ qubit. This makes the pokemon qubit more protected. For instance, the relaxation of the pokemon qubit is exponentially reduced by two equally important factors, while the relaxation of the 0-$\pi$ qubit is exponentially reduced by only one factor. Moreover, we show that the inductor in the pokemon can be replaced by a nonlinear inductor using, e.g., a pair or two pairs of Josephson junctions. This offers an experimentally promising way to implement next-generation superconducting qubits with even higher quantum coherence.