  In statistical mechanics, computing the partition function is generally
difficult. An approximation method using a variational autoregressive network
(VAN) has been proposed recently. This approach offers the advantage of
directly calculating the generation probabilities while obtaining a
significantly large number of samples. The present study introduces a novel
approximation method that employs samples derived from quantum annealing
machines in conjunction with VAN, which are empirically assumed to adhere to
the Gibbs-Boltzmann distribution. When applied to the finite-size
Sherrington-Kirkpatrick model, the proposed method demonstrates enhanced
accuracy compared to the traditional VAN approach and other approximate
methods, such as the widely utilized naive mean field.
