Benchmarking quantum simulation costs for many-body models

Quantum computers offer the potential to efficiently simulate the dynamics of quantum systems, a task whose difficulty scales exponentially with system size on classical devices. To assess the potential for near-term quantum computers to simulate many-body systems we compare two significant measures of computational cost, the maximum Pauli depth and a bound on the number of Trotter steps needed to accurately simulate the system's time evolution, for two prominent and closely related many-body models, the Hubbard and the t-J model. We find that, despite the t-J model possessing a substantially smaller Hilbert space than the Hubbard model, its maximum Pauli depth is significantly larger. Alternatively, the optimal choice of model for minimizing the number of Trotter steps depends heavily on the model parameters.