Abstract
Mainstream machine-learning techniques such as deep learning and probabilistic programming rely heavily on sampling from generally intractable probability distributions. There is increasing interest in the potential advantages of using quantum computing technologies as sampling engines to speed up these tasks or to make them more effective. However, some pressing challenges in state-of-the-art quantum annealers have to be overcome before we can assess their actual performance. The sparse connectivity, resulting from the local interaction between quantum bits in physical hardware implementations, is considered the most severe limitation to the quality of constructing powerful generative unsupervised machine-learning models. Here we use embedding techniques to add redundancy to data sets, allowing us to increase the modeling capacity of quantum annealers. We illustrate our findings by training hardware-embedded graphical models on a binarized data set of handwritten digits and two synthetic data sets in experiments with up to 940 quantum bits. Our model can be trained in quantum hardware without full knowledge of the effective parameters specifying the corresponding quantum Gibbs-like distribution; therefore, this approach avoids the need to infer the effective temperature at each iteration, speeding up learning; it also mitigates the effect of noise in the control parameters, making it robust to deviations from the reference Gibbs distribution. Our approach demonstrates the feasibility of using quantum annealers for implementing generative models, and it provides a suitable framework for benchmarking these quantum technologies on machine-learning-related tasks.
Highlights
Sampling from high-dimensional probability distributions is at the core of a wide spectrum of machine-learning techniques with important applications across science, engineering, and society; deep learning [1] and probabilistic programming [2] are some notable examples
V, we describe the experiments performed on two synthetic data sets and a coarsegrained binarized version of the OptDigits data set; we show that the model introduced here, trained by using the D-Wave 2X (DW2X) hosted at NASA Ames Research Center, displays good generative properties and can reconstruct and classify data with good accuracy
The first task we address is verifying that the model is able to learn the joint probability distribution of variables given a data set
Summary
Sampling from high-dimensional probability distributions is at the core of a wide spectrum of machine-learning techniques with important applications across science, engineering, and society; deep learning [1] and probabilistic programming [2] are some notable examples. An approach to unsupervised learning is to model the joint probability distribution of all the variables of interest. This is known as the generative approach. Generative models find application in anomaly detection, reinforcement learning, handling of missing values, and visual arts, to name a few [4]. Generative models rely on a sampling engine that is used for both inference and learning. Because of the intractability of traditional sampling techniques like the Markov chain Monte Carlo (MCMC) method, finding good generative models is among the hardest problems in machine learning [1,3,6,7,8]
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