Fast, accurate, high-resolution simulation of large-scale Fermi-Hubbard models on a digital quantum processor

Abstract

We report experimental digital quantum simulation of the one-dimensional Fermi-Hubbard model on a superconducting quantum processor at a scale beyond the reach of exact statevector simulation and challenging for state-of-the-art tensor-network methods. We encode this problem using up to 120 qubits through an efficient mapping that reduces circuit complexity, and we improve accuracy through error suppression to simulate dynamical evolution using up to 90 Trotter steps. From a vacancy defect introduced in the middle of an $L=31$-site (62-qubit) Néel initial state, we directly observe spin-charge separation to $t=9$ in natural units and quantitatively extract velocities $v_c$, $v_s$, which match classical simulations across model parameters, and analytics in appropriate regimes. We then extend experiments to $L=60$ fermions (120 qubits) and evolution times to $t=6$ using 30 Trotter steps. Quantum-processor outputs agree quantitatively with approximate classical simulations performed using a time-dependent variational principle (TDVP) solver and we observe that increasing the TDVP bond dimension through $χ= 4096$ expands the range of evolution times within which agreement has RMSE $\sim 1\%$ before the approaches diverge. Owing to the large scale of the simulation and the use of overhead-free error-suppression techniques, for simulated evolution times at the limit of quantum/classical agreement ($t\gtrsim 5$ in natural hopping units), the wall-clock runtime of the quantum processor is nearly three orders of magnitude faster than TDVP simulations with $χ= 4096$ and implemented using the ITensor and TeNPy packages. These results establish contemporary digital quantum processors as a versatile, quantitatively accurate, and competitive platform for the study of fermionic many-body dynamics in regimes where leading classical methods can become prohibitively expensive.