Gate-efficient simulation of molecular eigenstates on a superconducting qubit quantum computer

A key requirement to perform simulations of large quantum systems on current quantum processors is the design of quantum algorithms with short circuit depth. To achieve this, it is essential to realize a gate set that is tailored to the problem at hand and which can be directly implemented in hardware [P. Barkoutsos et al., Phys. Rev. A 98, 022322 (2018)]. Here, we experimentally demonstrate that exchange-type gates are ideally suited for calculations in quantum chemistry [M. Ganzhorn et al., arXiv:1809.05057]. We determine the energy spectrum of molecular hydrogen using a variational quantum eigensolver algorithm based on exchange-type gates in combination with a method from computational chemistry to compute the excited states. 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.