Majorana string simulation of nonequilibrium dynamics in two-dimensional lattice fermion systems

The study of real-time dynamics of fermions remains one of the last frontiers beyond the reach of classical simulations and is key to our understanding of quantum behavior in chemistry and materials, with implications for quantum technology. Here we introduce a Heisenberg-picture algorithm that propagates observables expressed in a Majorana-string basis using a truncation scheme that preserves Trotter accuracy and aims at maintaining computational efficiency. The framework is exact for quadratic Hamiltonians--remaining restricted to a fixed low-weight sector determined by the physical observable--admits variational initial states, and can be extended to interacting regimes via systematically controlled truncations. We benchmark our approach on one- and two-dimensional Fermi-Hubbard quenches, comparing against tensor network methods (MPS and fPEPS) and recent experimental data. The method achieves high accuracy on timescales comparable to state-of-the-art variational techniques and experiments, demonstrating that controlled Majorana-string truncation is a practical tool for simulating two-dimensional fermionic dynamics.