Automating Quantization and Diagonalization of Superconducting Circuits

The analysis of superconducting circuits currently consists of a multi-step process combining analytical and numerical elements that together enable the transition from a lumped-element circuit diagram to a quantum Hamiltonian ready to be diagonalized. Important aspects include the choice of appropriate circuit variables, incorporation of constraints imposed by Kirchhoff's laws, the elimination of cyclic variables, and the distinction of degrees of freedom subject to periodic versus confining boundary conditions upon quantization. We present work that systematizes these steps in a manner amenable to algorithmic implementation, thus opening the pathway for streamlined and efficient analysis of unexplored superconducting circuits to serve as qubits, tunable couplers, and similar parts of quantum processors. A concrete implementation of this circuit quantization tool is made available as an extension to the open-source scqubits package.