Determine mixing times beyond the simulated Hubbard systems

Determine the mixing time required for convergence of the single-ancilla Lindblad ground-state preparation algorithm for Hubbard models beyond the system sizes simulated in the paper, including its dependence on the choice of mixing operators, system parameters, and lattice geometry.

Background

The resource estimates for larger Hubbard systems depend critically on the mixing time of the Lindblad dynamics, because the total number of steps grows quadratically with the mixing time. The paper obtains mixing-time data only for small simulated systems and uses extrapolation for larger systems.

The authors explicitly state that the mixing time cannot readily be predicted beyond the simulated systems and that it depends on the mixer, Hamiltonian parameters, and geometry. Establishing reliable bounds or scaling laws would therefore be necessary for quantitative resource estimates and for assessing the practical feasibility of Lindblad-based ground-state preparation.