  In an attempt to better leverage superconducting quantum computers, scaling
efforts have become the central concern. These efforts have been further
exacerbated by the increased complexity of these circuits. The added complexity
can introduce parasitic couplings and resonances, which may hinder the overall
performance and scalability of these devices. We explore a method of modeling
and characterization based on multiport impedance functions that correspond to
multi-qubit circuits. By combining vector fitting techniques with a novel
method for interconnecting rational impedance functions, we are able to
efficiently construct Hamiltonians for multi-qubit circuits using
electromagnetic simulations. Our methods can also be applied to circuits that
contain both lumped and distributed element components. The constructed
Hamiltonians account for all the interactions within a circuit that are
described by the impedance function. We then present characterization methods
that allow us to estimate effective qubit coupling rates, state-dependent
dispersive shifts of resonant modes, and qubit relaxation times.
