  We investigate the quantum effect on machine learning (ML) models exemplified
by the Generative Adversarial Network (GAN), which is a promising deep learning
framework. In the general GAN framework the generator maps uniform noise to a
fake image. In this study, we utilize the Associative Adversarial Network
(AAN), which consists of a standard GAN and an associative memory. Further, we
set a Boltzmann Machine (BM), which is an undirected graphical model that
learns low-dimensional features extracted from a discriminator, as the memory.
Owing to difficulty calculating the BM's log-likelihood gradient, it is
necessary to approximate it by using the sample mean obtained from the BM,
which has tentative parameters. To calculate the sample mean, a Markov Chain
Monte Carlo (MCMC) is often used. In a previous study, this was performed using
a quantum annealer device, and the performance of the "Quantum" AAN was
compared to that of the standard GAN. However, its better performance than the
standard GAN is not well understood. In this study, we introduce two methods to
draw samples: classical sampling via MCMC and quantum sampling via quantum
Monte Carlo (QMC) simulation, which is quantum simulation on the classical
computer. Then, we compare these methods to investigate whether quantum
sampling is advantageous. Specifically, calculating the discriminator loss, the
generator loss, inception score and Fr\'echet inception distance, we discuss
the possibility of AAN. We show that the AANs trained by both MCMC and QMC are
more stable during training and produce more varied images than the standard
GANs. However, the results indicate no difference in sampling by QMC simulation
compared to that by MCMC.
