  Resolving quantum many-body problems represents one of the greatest
challenges in physics and physical chemistry, due to the prohibitively large
computational resources that would be required by using classical computers. A
solution has been foreseen by directly simulating the time evolution through
sequences of quantum gates applied to arrays of qubits, i.e. by implementing a
digital quantum simulator. Superconducting circuits and resonators are emerging
as an extremely-promising platform for quantum computation architectures, but a
digital quantum simulator proposal that is straightforwardly scalable,
universal, and realizable with state-of-the-art technology is presently
lacking. Here we propose a viable scheme to implement a universal quantum
simulator with hybrid spin-photon qubits in an array of superconducting
resonators, which is intrinsically scalable and allows for local control. As
representative examples we consider the transverse-field Ising model, a spin-1
Hamiltonian, and the two-dimensional Hubbard model; for these, we numerically
simulate the scheme by including the main sources of decoherence. In addition,
we show how to circumvent the potentially harmful effects of inhomogeneous
broadening of the spin systems.
