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The efficient simulation of correlated quantum systems is the most promisingnear-term application of quantum computers. Here, we present a measurement ofthe second Renyi entropy of the ground state of the two-site Fermi-Hubbardmodel on a $5$-qubit programmable quantum computer based on trapped ions. Ourwork illustrates the extraction of a non-linear characteristic of a quantumstate using a controlled-swap gate acting on two copies of the state. Thisscalable measurement of entanglement on a universal quantum computer will, withmore qubits, provide insights into many-body quantum systems that areimpossible to simulate on classical computers.

Measuring the Renyi entropy of a two-site Fermi-Hubbard model on a trapped ion quantum computer