  The development of quantum-classical hybrid (QCH) algorithms is critical to
achieve state-of-the-art computational models. A QCH variational autoencoder
(QVAE) was introduced in Ref. [1] by some of the authors of this paper. QVAE
consists of a classical auto-encoding structure realized by traditional deep
neural networks to perform inference to, and generation from, a discrete latent
space. The latent generative process is formalized as thermal sampling from
either a quantum or classical Boltzmann machine (QBM or BM). This setup allows
quantum-assisted training of deep generative models by physically simulating
the generative process with quantum annealers. In this paper, we have
successfully employed D-Wave quantum annealers as Boltzmann samplers to perform
quantum-assisted, end-to-end training of QVAE. The hybrid structure of QVAE
allows us to deploy current-generation quantum annealers in QCH generative
models to achieve competitive performance on datasets such as MNIST. The
results presented in this paper suggest that commercially available quantum
annealers can be deployed, in conjunction with well-crafted classical deep
neutral networks, to achieve competitive results in unsupervised and
semisupervised tasks on large-scale datasets. We also provide evidence that our
setup is able to exploit large latent-space (Q)BMs, which develop slowly mixing
modes. This expressive latent space results in slow and inefficient classical
sampling, and paves the way to achieve quantum advantage with quantum annealing
in realistic sampling applications.
