Benchmarking Adaptive Variational Quantum Eigensolvers

• Main Authors: Daniel Claudino, Jerimiah Wright, Alexander J. McCaskey, Travis S. Humble
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2020-12-01
• Series: Frontiers in Chemistry
• Subjects: ADAPT-VQE; quantum computing; quantum chemistry; VQE; potential energy scan; state fidelity
• Online Access: https://www.frontiersin.org/articles/10.3389/fchem.2020.606863/full

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.