Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model

Quantum spin systems may offer the first opportunities for beyond-classical quantum computations of scientific interest. While general quantum simulation algorithms likely require error-corrected qubits, there may be applications of scientific interest prior to the practical implementation of quantum error correction. The variational quantum eigensolver (VQE) is a promising approach to finding energy eigenvalues on noisy quantum computers. Lattice models are of broad interest for use on near-term quantum hardware due to the sparsity of the number of Hamiltonian terms and the possibility of matching the lattice geometry to the hardware geometry. Here, we consider the Kitaev spin model on a hardware-native square-octagon qubit connectivity map, and examine the possibility of efficiently probing its rich phase diagram with VQE approaches. By benchmarking different choices of variational Ansatz states and classical optimizers, we illustrate the advantage of a mixed optimization approach using the Hamiltonian variational Ansatz (HVA) and the potential of probing the system's phase diagram using VQE. We further demonstrate the implementation of HVA circuits on Rigetti's Aspen-9 chip with error mitigation.