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.
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