  A key requirement to perform simulations of large quantum systems on
near-term quantum hardware is the design of quantum algorithms with short
circuit depth that finish within the available coherence time. A way to stay
within the limits of coherence is to reduce the number of gates by implementing
a gate set that matches the requirements of the specific algorithm of interest
directly in hardware. Here, we show that exchange-type gates are a promising
choice for simulating molecular eigenstates on near-term quantum devices since
these gates preserve the number of excitations in the system. Complementing the
theoretical work by Barkoutsos et al. [PRA 98, 022322 (2018)], we report on the
experimental implementation of a variational algorithm on a superconducting
qubit platform to compute the eigenstate energies of molecular hydrogen. We
utilize a parametrically driven tunable coupler to realize exchange-type gates
that are configurable in amplitude and phase on two fixed-frequency
superconducting qubits. With gate fidelities around 95% we are able to compute
the eigenstates within an accuracy of 50 mHartree on average, a limit set by
the coherence time of the tunable coupler.
