Simulating the Fermi-Hubbard model with long-range hopping on a quantum computer

We investigate the performance and accuracy of digital quantum algorithms for the study of static and dynamic properties of the fermionic Hubbard model at half-filling with next-nearest neighbour hopping terms. We provide quantum circuits to perform ground and excited states calculations, via the Variational Quantum Eigensolver (VQE) and the Quantum Equation of Motion (qEOM) approach respectively, as well as product formulas decompositions for time evolution. We benchmark our approach on a chain with L=6 sites and periodic boundary conditions, computing the charge and spin gaps, the spectral function and spin-spin dynamic correlations. Our results for the ground state phase diagram are in qualitative agreement with known results in the thermodynamic limit. Finally, we provide concrete scalings for the number of gates needed to implement our protocols on a qubit register with all-to-all connectivities and on a heavy hexagonal coupling map.