  For superconducting quantum processors consisting of low anharmonicity qubits
such as transmons we give a complete microwave description of the system in the
qubit subspace. We assume that the qubits are dispersively coupled to a
distributed microwave structure such that the detunings of the qubits from the
internal modes of the microwave structure are stronger than their couplings. We
define qubit ports across the terminals of the Josephson junctions and drive
ports where transmission lines carrying drive signals reach the chip and we
obtain the multiport impedance response of the linear passive part of the
system between the ports. We then relate interaction parameters in between
qubits and between the qubits and the environment to the entries of this
multiport impedance function: in particular we show that the exchange coupling
rate J between qubits is related in a simple way to the off-diagonal entry
connecting the qubit ports. Similarly we relate couplings of the qubits to
voltage drives and lossy environment to the entries connecting the qubits and
the drive ports. Our treatment takes into account all the modes (possibly
infinite) that might be present in the distributed electromagnetic structure
and provides an efficient method for the modeling and analysis of the circuits.
