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The development of quantum-classical hybrid (QCH) algorithms is critical toachieve state-of-the-art computational models. A QCH variational autoencoder(QVAE) was introduced in Ref. [1] by some of the authors of this paper. QVAEconsists of a classical auto-encoding structure realized by traditional deepneural networks to perform inference to, and generation from, a discrete latentspace. The latent generative process is formalized as thermal sampling fromeither a quantum or classical Boltzmann machine (QBM or BM). This setup allowsquantum-assisted training of deep generative models by physically simulatingthe generative process with quantum annealers. In this paper, we havesuccessfully employed D-Wave quantum annealers as Boltzmann samplers to performquantum-assisted, end-to-end training of QVAE. The hybrid structure of QVAEallows us to deploy current-generation quantum annealers in QCH generativemodels to achieve competitive performance on datasets such as MNIST. Theresults presented in this paper suggest that commercially available quantumannealers can be deployed, in conjunction with well-crafted classical deepneutral networks, to achieve competitive results in unsupervised andsemisupervised tasks on large-scale datasets. We also provide evidence that oursetup is able to exploit large latent-space (Q)BMs, which develop slowly mixingmodes. This expressive latent space results in slow and inefficient classicalsampling, and paves the way to achieve quantum advantage with quantum annealingin realistic sampling applications.

A Path Towards Quantum Advantage in Training Deep Generative Models with Quantum Annealers