Quantum Simulation of 1D & 2D Lattice-based Fermi Hubbard Model using Variational Quantum Algorithms

Quantum simulation and near-term quantum algorithms have gained significant momentum over the past few years, with researchers exploring quantum-based approaches to solve classically intractable problems. Out of many research problems, certain problems are well suited for quantum algorithms. Fermi Hubbard model based on lattice structures is one of the quantum-mechanical models used in many-body and condensed matter physics to capture the essence of electron-correlated systems. In this work, we show one of the first kinds of experiments on simulating the ground state properties of 1D and 2D Fermi Hubbard-based lattice models compared with the reference ground state energy values using Qiskit Nature. We utilize the Variational Quantum Eigensolver (VQE) and different gradient-based optimizers to achieve results that closely converge towards the exact values, showcasing the potential of variational quantum algorithms.