  We propose a digital-analog quantum simulation of generalized Dicke models
with superconducting circuits, including Fermi-Bose condensates, biased and
pulsed Dicke models, for all regimes of light-matter coupling. We encode these
classes of problems in a set of superconducting qubits coupled with a bosonic
mode implemented by a transmission line resonator. Via digital-analog
techniques, an efficient quantum simulation can be performed in
state-of-the-art circuit quantum electrodynamics platforms, by suitable
decomposition into analog qubit-bosonic blocks and collective single-qubit
pulses through digital steps. Moreover, just a single global analog block would
be needed during the whole protocol in most of the cases, superimposed with
fast periodic pulses to rotate and detune the qubits. Therefore, a large number
of digital steps may be attained with this approach, providing a reduced
digital error. Additionally, the number of gates per digital step does not grow
with the number of qubits, rendering the simulation efficient. This strategy
paves the way for the scalable digital-analog quantum simulation of many-body
dynamics involving bosonic modes and spin degrees of freedom with
superconducting circuits.
