Strategies for solving the Fermi-Hubbard model on near-term quantum computers

One of the main applications of near-term quantum computers is expected to be solving many-body quantum systems. The present study reports on extensive optimization and numerical investigation of the Variational Quantum Eigensolver method for the iconic Fermi-Hubbard model, including the effect of realistic measurements and noise. The presented optimized circuits use up to an order of magnitude fewer gates than previously reported, suggesting that quantum circuits with a gate depth substantially below 1000 could be sufficient to solve instances beyond the capacity of classical exact diagonalization.