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

Abstract

We establish new theoretical results demonstrating the efficiency and robustness of system-bath interaction algorithms for quantum thermal and ground state preparation. We rigorously show that, even when the coupling strength is chosen independently of the desired accuracy, the induced quantum channel admits the target thermal and ground states as approximate fixed points with arbitrarily high precision. This contrasts with prior analyses, which typically rely on the leading order Lindbladian approximation and require the coupling strength to decrease polynomially with the target error tolerance. Our proof introduces new techniques for controlling all orders of the Dyson expansion and for analyzing the associated multidimensional operator Fourier transforms. Building on these new estimation, we demonstrate an improved end-to-end complexity analysis of thermal and ground state preparation for the system-bath interaction algorithms. 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.