Modeling Superconducting Quantum Circuit Systems

In a general aspect, a superconducting quantum circuit system is modeled. In some aspects, a graph representing a quantum circuit system is generated. The graph includes vertices and edges; the edges represent circuit elements of the quantum circuit system, and the vertices represent physical connections between the circuit elements. Inverse inductances, conductances, capacitances, and junction inverse inductances are assigned to respective edges of the graph based on a lumped-element approximation of the quantum circuit system. A coordinate system is determined based on the graph, and a matrix representation of the system is determined based on the coordinate system. A Hamiltonian for the quantum circuit system is determined using the matrix representation, and the quantum circuit system is simulated based on the Hamiltonian.