Benchmarking VQE for the square-octagon-lattice Kitaev model

The variational quantum eigensolver (VQE) is a promising apporoach to find eigenstates and eigenenergies on NISQ devices. In this presentation, we consider the Kitaev spin model with a square-octagon lattice geometry that matches the connectivity map of Rigetti's QPUs. The hardware-native geometry allows the possibility of efficiently exploring the spin model's rich phase diagram with the VQE approach. We will illustrate the advantage of a mixed optimization approach using the Hamiltonian variational ansatz (HVA) by benchmarking several choices of variational ansatzes and classical optimizers. We will also demonstrate the implementation of a proof-of-principle HVA circuit on the Rigetti's Aspen-9 QPU with appropriate error mitigation techniques.