Enumeration of all superconducting circuits up to 5 nodes

The most popular superconducting qubits today, the transmon and fluxonium, are relatively small circuits consisting of a Josephson junction in parallel with a capacitor or inductor respectively. Although these systems have shown incredible progress, they lack the intrinsic noise protection that is possible with larger, multi-mode circuits. While there already exist compelling proposals for novel noise protected qubits, the best circuits may yet remain undiscovered, due to the incredibly large search space of possible configurations. I will present a technique for enumerating all possible superconducting circuits constructed of capacitors, inductors, and Josephson junctions, plus share results from a search over all possible three node circuits for novel superconducting qubits.