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.
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BibTeX
@misc{ohzeki2026boundarycanceled,
title = {{Boundary-Canceled Score-Hamiltonian Sampling}},
author = {Masayuki Ohzeki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.05904},
eprint = {2609.05904},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05904},
}
RIS
TY - UNPB
TI - Boundary-Canceled Score-Hamiltonian Sampling
AU - Masayuki Ohzeki
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2609.05904
UR - https://arxiv.org/abs/2609.05904
AB - 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.
ER -