AUTHOR=Claudino Daniel , Wright Jerimiah , McCaskey Alexander J. , Humble Travis S. TITLE=Benchmarking Adaptive Variational Quantum Eigensolvers JOURNAL=Frontiers in Chemistry VOLUME=8 YEAR=2020 URL=https://www.frontiersin.org/journals/chemistry/articles/10.3389/fchem.2020.606863 DOI=10.3389/fchem.2020.606863 ISSN=2296-2646 ABSTRACT=

By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H2, NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.