  We propose a digital-analog quantum algorithm for simulating the
Hubbard-Holstein model, describing strongly-correlated fermion-boson
interactions, in a suitable architecture with superconducting circuits. It
comprises a linear chain of qubits connected by resonators, emulating
electron-electron (e-e) and electron-phonon (e-p) interactions, as well as
fermion tunneling. Our approach is adequate for a digital-analog quantum
computing (DAQC) of fermion-boson models including those described by the
Hubbard-Holstein model. We show the reduction in the circuit depth of the DAQC
algorithm, a sequence of digital steps and analog blocks, outperforming the
purely digital approach. We exemplify the quantum simulation of a half-filling
two-site Hubbard-Holstein model. In such example we obtain fidelities larger
than 0.98, showing that our proposal is suitable to study the dynamical
behavior of solid-state systems. Our proposal opens the door to computing
complex systems for chemistry, materials, and high-energy physics.
