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Quantum annealing (QA) is a hardware-based heuristic optimization and sampling method applicable to discrete undirected graphical models. While similar to simulated annealing, QA relies on quantum, rather than thermal, effects to explore complex search spaces. For many classes of problems, QA is known to offer computational advantages over simulated annealing. Here we report on the ability of recent QA hardware to accelerate training of fully visible Boltzmann machines. We characterize the sampling distribution of QA hardware, and show that in many cases, the quantum distributions differ significantly from classical Boltzmann distributions. In spite of this difference, training (which seeks to match data and model statistics) using standard classical gradient updates is still effective. We investigate the use of QA for seeding Markov chains as an alternative to contrastive divergence (CD) and persistent contrastive divergence (PCD). Using $k=50$ Gibbs steps, we show that for problems with high-energy barriers between modes, QA-based seeds can improve upon chains with CD and PCD initializations. For these hard problems, QA gradient estimates are more accurate, and allow for faster learning. Furthermore, and interestingly, even the case of raw QA samples (that is, $k=0$) achieved similar improvements. We argue that this relates to the fact that we are training a quantum rather than classical Boltzmann distribution in this case. The learned parameters give rise to hardware QA distributions closely approximating classical Boltzmann distributions that are hard to train with CD/PCD.
Generative modeling with machine learning has provided a new perspective on the data-driven task of reconstructing quantum states from a set of qubit measurements. As increasingly large experimental quantum devices are built in laboratories, the ques
Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core of which
We present a real-world application that uses a quantum computer. Specifically, we train a RBM using QA for cybersecurity applications. The D-Wave 2000Q has been used to implement QA. RBMs are trained on the ISCX data, which is a benchmark dataset fo
Restricted Boltzmann machines are undirected neural networks which have been shown to be effective in many applications, including serving as initializations for training deep multi-layer neural networks. One of the main reasons for their success is
We introduce a methodology for generating benchmark problem sets for Ising machines---devices designed to solve discrete optimization problems cast as Ising models. In our approach, linear systems of equations are cast as Ising cost functions. While