Boundary-Canceled Score-Hamiltonian Sampling

Abstract

Diffusion sampling is related to imaginary-time quantum annealing through a forward/backward Schrödinger equation pair and its one-sided counterdiabatic connection. For a smooth, gapped Score-Hamiltonian path, the exact connection transports the target density at any evolution time. We apply quantum-annealing performance analysis to residuals from approximating this connection with a trained score. If the first $r$ terminal schedule derivatives vanish, the squared Hellinger error scales as $T^{-2r-2}$, with a prefactor determined by the terminal learning residual and inverse gaps. Direct two-dimensional imaginary-time evolution with one fixed neural score reproduces these powers and prefactors. Terminal schedule design thus suppresses the distributional effect of imperfect score learning without retraining the network.

arXiv comment4 pages, 1 figure