Simulating quantum physics with a device which itself is quantum mechanical,a notion Richard Feynman originated, would be an unparallelled computationalresource. However, the universal quantum simulation of fermionic systems isdaunting due to their particle statistics, and Feynman left as an open questionwhether it could be done, because of the need for non-local control. Here, weimplement fermionic interactions with digital techniques in a superconductingcircuit. Focusing on the Hubbard model, we perform time evolution with constantinteractions as well as a dynamic phase transition with up to four fermionicmodes encoded in four qubits. The implemented digital approach is universal andallows for the efficient simulation of fermions in arbitrary spatialdimensions. We use in excess of 300 single-qubit and two-qubit gates, and reachglobal fidelities which are limited by gate errors. This demonstrationhighlights the feasibility of the digital approach and opens a viable routetowards analog-digital quantum simulation of interacting fermions and bosons inlarge-scale solid state systems.
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