Using a quantum simulator to benchmark a novel efficient approximation algorithm for localized 1D Fermi-Hubbard systems

Identifying and understanding the applications of NISQ-era quantum simulators and quantum computers is a topical problem. Quantum many-body physics embodies a unique set of problems that are both computationally hard and physically pertinent and are therefore apt for applications of NISQ devices. While state-of-the art neutral atom quantum simulators have made remarkable progress in studying many-body dynamics, they are noisy and limited in the variability of initial state and the observables that can be measured. Here we show that despite these limitations, quantum simulators can be used to develop new numerical techniques to solve for the dynamics of many-body systems in regimes that are practically inaccessible to established numerical techniques [1]. Considering localized 1D Fermi-Hubbard systems, we use an approximation ansatz to develop a new numerical method that facilitates efficient classical simulations in such regimes. Since this new method does not have an error estimate and is not valid in general, we use a neutral-atom quantum simulator with L_exp = 290 lattice sites to benchmark its performance in terms of accuracy and convergence for evolution times up to 700 tunnelling times. We then use this method to make a prediction of the behaviour of interacting dynamics for spin-imbalanced Fermi-Hubbard systems, which we show to be in quantitative agreement with experimental results. Finally, we demonstrate that the convergence of our method is the slowest when the entanglement depth developed in the many-body system is neither too small nor too large. This represents a promising regime for near-term applications of quantum simulators.