  Simulating quantum physics with a device which itself is quantum mechanical,
a notion Richard Feynman originated, would be an unparallelled computational
resource. However, the universal quantum simulation of fermionic systems is
daunting due to their particle statistics, and Feynman left as an open question
whether it could be done, because of the need for non-local control. Here, we
implement fermionic interactions with digital techniques in a superconducting
circuit. Focusing on the Hubbard model, we perform time evolution with constant
interactions as well as a dynamic phase transition with up to four fermionic
modes encoded in four qubits. The implemented digital approach is universal and
allows for the efficient simulation of fermions in arbitrary spatial
dimensions. We use in excess of 300 single-qubit and two-qubit gates, and reach
global fidelities which are limited by gate errors. This demonstration
highlights the feasibility of the digital approach and opens a viable route
towards analog-digital quantum simulation of interacting fermions and bosons in
large-scale solid state systems.
