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We propose the simulation of quantum-optical systems in the ultrastrong-coupling regime using a variational quantum algorithm. More precisely, we introduce a short-depth variational form to prepare the ground state of the multimode Dicke model on a quantum processor and present proof-of-principle results obtained using an IBM device. We moreover provide an algorithm for characterizing the ground state by Wigner state tomography. Our work is a first step toward digital quantum simulation of light-matter systems with potential applications to few-impurity spin-boson models.