Benchmarking adaptive variational quantum eigensolvers

TL;DR

This paper benchmarks the accuracy and robustness of variational quantum eigensolvers, especially ADAPT-VQE, in calculating electronic ground states of diatomic molecules, highlighting optimization strategies and error trends.

Contribution

It provides a comparative analysis of VQE and ADAPT-VQE methods for molecular ground state calculations, emphasizing ADAPT-VQE's robustness and optimization efficiency.

Findings

ADAPT-VQE is more robust to optimization variations.

Gradient-based optimization outperforms gradient-free methods.

Errors increase with molecular size.

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 H$_2$, 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.