1. A method of determining physical operating parameters of a quantum information processing circuit, the method comprising: by operation of a design tool executed by one or more processors in a computer system, generating a circuit specification for a quantum information processing circuit comprising a qubit device; storing the circuit specification in a memory of the computer system; loading the circuit specification from the memory into a workspace of an electromagnetic structure solver executed by one or more processors in the computer system; by operation of the electromagnetic structure solver, analyzing the quantum information processing circuit to obtain a linear response function of the quantum information processing circuit, wherein the linear response function represents a linear component of the quantum information processing circuit, and wherein obtaining the linear response function comprises imposing a passivity condition and a positive real condition on a fitted linear response function; storing the linear response function in the memory of the computer system; and by operation of a quantum circuit analysis tool executed by one or more processors in the computer system: accessing the linear response function from the memory; determining circuit parameters of a multi-mode resonator circuit based on the linear response function and a circuit topology of the multi-mode resonator circuit, wherein the circuit parameters of the multi-mode resonator circuit are determined using a Brune circuit synthesis algorithm; generating a linear circuit model based on the circuit parameters and the circuit topology, wherein the linear circuit model comprises a first Hamiltonian representing the multi-mode resonator circuit; generating a composite circuit model based on combining the linear circuit model and a nonlinear circuit model, the nonlinear circuit model comprising a second Hamiltonian representing a nonlinear component in the quantum information processing circuit, wherein generating the composite circuit model comprises generating a composite Hamiltonian by combining the first Hamiltonian with the second Hamiltonian; computing a numerical solution to the Schrödinger equation for the composite Hamiltonian, wherein the numerical solution comprises at least three quantum energy levels of the qubit device in the quantum information processing circuit; extracting physical operating parameters of the quantum information processing circuit from the numerical solution to the Schrödinger equation, wherein the physical operating parameters include a coherence time of the qubit device and a resonance frequency of the qubit device; and storing the physical operating parameters in the memory of the computer system; by operation of the design tool, modifying the circuit specification based on the physical operating parameters; and manufacturing a quantum processor chip based on the modified circuit specification.