The 0-{pi} qubit promises longer lifetimes than the transmon, making it a strong candidate for a next-generation, lower-error qubit. Gyenis et al. experimentally demonstrated an unprotectedsingle-qubit gate in the soft 0-{\pi} regime [1], but no corresponding two-qubit gate has yet been proposed. We propose an unprotected CZ gate for capacitively coupled soft 0-{\pi} qubits. The gate uses a direct transition between a computational state and a higher non-computational state. Assuming negligible device disorder and a phenomenological noise model, the simulated CZ gate achieves a fidelity of approximately 99.9% at a gate time of approximately 160 ns.
Nonlinear superconducting circuits can be used as amplifiers, transducers, and qubits. Only a handful of superconducting circuits have been analyzed or built, so many high-performingconfigurations likely remain undiscovered. We seek to catalog this design space by enumerating all superconducting circuits — up to five nodes in size — built of capacitors, inductors, and Josephson junctions. Using graph isomorphism, we remove redundant configurations to construct a set of unique circuits. We define the concept of a „Hamiltonian class“ and sort the resulting circuit Hamiltonians based on the types of variables present and the structure of their coupling. Finally, we search for novel superconducting qubits by explicitly considering all three node circuits, showing how the results of our enumeration can be used as a starting point for circuit design tasks.