Compact fermionic encodings on a trapped-ion quantum computer for the 2D Fermi-Hubbard model

The spinful Fermi-Hubbard model (FHM) is crucial for understanding strongly correlated electronic systems like high-temperature superconducting cuprates. However, exact numerical diagonalization scales exponentially, and approximate classical simulations face the NP-hard "sign problem." While digital quantum computers can address this, realizations have been limited to quasi-1D models since Jordan-Wigner transformation yields large Pauli weight operators beyond 1D. Here, we simulate the 2D spinful FHM on 2x4 and 3x4 lattices using 20 and 30 qubits respectively on IonQ's ion-trap processor, exploiting all-to-all qubit connectivity. We employ local Compact Fermion-to-Qubit Encoding to avoid mapping local fermionic operators to non-local large-weight Pauli operators in 2D. Crucially, we characterize the trade-off between Trotter error during Hamiltonian time-evolution and accumulated two-qubit gate error across Trotter steps. Through parameter optimization minimizing systematic errors, we observe long-range antiferromagnetic order in the 2D half-filled lattice, consistent with ground state predictions. These effects vanish upon hole-doping, indicating paramagnetic phase. We observe separated charge and spin dynamics in the 2x4 quarter-filled lattice. Our work presents benchmark results in the simulation of spinful 2D Fermi-Hubbard systems, and holds promise for developing and implementing scalable improved encodings for other strongly interacting quantum systems.