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

The efficient simulation of correlated quantum systems is the most promising near-term application of quantum computers. Here, we present the calculation 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 efficient mapping of the electronic system to the qubit Hilbert space, circuit compilation and implementation on a physical quantum computer, optimized use of finite quantum gate depth, extraction of a non-linear characteristic of a quantum state using the controlled-swap gate, and effective reduction of experimental errors by over 40% using a symmetry-based post-selection scheme. Thus we demonstrate the first scalable measurement of entanglement on a digital quantum computer, which on larger systems will provide insights into many-body quantum systems that are impossible to simulate on classical computers.