  Building a scalable quantum computer requires developing appropriate models
to understand and verify its complex quantum dynamics. We focus on
superconducting quantum processors based on transmons for which full numerical
simulations are already challenging at the level of qubytes. It is thus highly
desirable to develop accurate methods of modeling qubit networks that do not
rely solely on numerical computations. Using systematic perturbation theory to
large orders in the transmon regime, we derive precise analytic expressions of
the transmon parameters. We apply our results to the case of
parametrically-modulated transmons to study recently-implemented
parametrically-activated entangling gates.
