  The efficient simulation of correlated quantum systems is the most promising
near-term application of quantum computers. Here, we present a measurement of
the second Renyi entropy of the ground state of the two-site Fermi-Hubbard
model on a $5$-qubit programmable quantum computer based on trapped ions. Our
work illustrates the extraction of a non-linear characteristic of a quantum
state using a controlled-swap gate acting on two copies of the state. This
scalable measurement of entanglement on a universal quantum computer will, with
more qubits, provide insights into many-body quantum systems that are
impossible to simulate on classical computers.
