5
Quantum Boltzmann Machine

As we saw in Chapters 3 and 4, quantum annealing can be used to solve hard optimisation problems. However, the range of possible applications of quantum annealing is much wider than that. In this chapter, we will consider two distinct but related use cases that go beyond solving optimisation problems: sampling and training deep neural networks. Specifically, we will focus on the Quantum Boltzmann Machine (QBM) – a generative model that is a direct quantum annealing counterpart of the classical Restricted Boltzmann Machine (RBM), and the Deep Boltzmann Machine (DBM) – a class of deep neural networks composed of multiple layers of latent variables with connections between the layers but not between units within each layer.

We start by providing detailed descriptions of the classical RBM, including the corresponding training algorithm. Due to the fact that an RBM operates on stochastic binary activation units, one can establish the correspondence...