  Extracting the Hamiltonian of interacting quantum-information processing
systems is a keystone problem in the realization of complex phenomena and
large-scale quantum computers. The remarkable growth of the field increasingly
requires precise, widely-applicable, and modular methods that can model the
quantum electrodynamics of the physical circuits, and even of their more-subtle
renormalization effects. Here, we present a computationally-efficient method
satisfying these criteria. The method partitions a quantum device into compact
lumped or quasi-distributed cells. Each is first simulated individually. The
composite system is then reduced and mapped to a set of simple subsystem
building blocks and their pairwise interactions. The method operates within the
quasi-lumped approximation and, with no further approximation, systematically
accounts for constraints, couplings, parameter renormalizations, and
non-perturbative loading effects. We experimentally validate the method on
large-scale, state-of-the-art superconducting quantum processors. We find that
the full method improves the experimental agreement by a factor of two over
taking standard coupling approximations when tested on the most sensitive and
dressed Hamiltonian parameters of the measured devices.
