Beyond Lindblad Dynamics: Rigorous Guarantees for Thermal and Ground State Preservation under System Bath Interactions

We establish new theoretical results demonstrating the efficiency and robustness of system bath interaction models for quantum thermal and ground state preparation. Unlike prior analyses, which typically relies on the Lindblad limit and require vanishing coupling strengths o(1), we rigorously show that efficient state preparation remains possible far beyond this regime, even when the coupling strength is Θ(1). We first prove that even with constant coupling strength, the induced quantum channel still approximately fixes the target state. For thermal state preparation, we then develop a general perturbative framework that yields end to end complexity bounds outside weak coupling, and in particular proves that the mixing time scales as the inverse square of the coupling strength. This framework extends to broad Hamiltonian for which KMS detailed balance Lindbladians are known to mix. These bounds substantially improve upon prior results, and numerical simulations further confirm the robustness of the system bath interaction framework across both weak and strong coupling regimes.