Trainmon: a framework for reverse engineering potentials in superconducting Qubits

A framework named Trainmon is introduced to reverse-engineer a quantum potential well for superconducting qubits. Trainmon consists of parallel branches of identical Josephson junctions. The Hamiltonian for this circuit resembles a discrete cosine transform, which can be applied to mimic various potentials. This framework is applied to well-known qubit potentials such as Quarton and Fluxonium, and their Hamiltonians are extracted and solved to validate the transition frequencies and calculate the coherence times of both the original qubits and their Trainmon-based versions.