Restricted Boltzmann Machines for galaxy morphology classification with a quantum annealer

We present the application of Restricted Boltzmann Machines (RBMs) to the task of astronomical image classification using a quantum annealer built by D-Wave Systems. Morphological analysis of galaxies provides critical information for studying their formation and evolution across cosmic time scales. We compress the images using principal component analysis to fit a representation on the quantum hardware. Then, we train RBMs with discriminative and generative algorithms, including contrastive divergence and hybrid generative-discriminative approaches. We compare these methods to Quantum Annealing (QA), Markov Chain Monte Carlo (MCMC) Gibbs Sampling, Simulated Annealing (SA) as well as machine learning algorithms like gradient boosted decision trees. We find that RBMs implemented on D-wave hardware perform well, and that they show some classification performance advantages on small datasets, but they don't offer a broadly strategic advantage for this task. During this exploration, we analyzed the steps required for Boltzmann sampling with the D-Wave 2000Q, including a study of temperature estimation, and examined the impact of qubit noise by comparing and contrasting the original D-Wave 2000Q to the lower-noise version recently made available. While these analyses ultimately had minimal impact on the performance of the RBMs, we include them for reference.

Application of Quantum Annealing to Training of Deep Neural Networks

In Deep Learning, a well-known approach for training a Deep Neural Network starts by training a generative Deep Belief Network model, typically using Contrastive Divergence (CD), then fine-tuning the weights using backpropagation or other discriminative techniques. However, the generative training can be time-consuming due to the slow mixing of Gibbs sampling. We investigated an alternative approach that estimates model expectations of Restricted Boltzmann Machines using samples from a D-Wave quantum annealing machine. We tested this method on a coarse-grained version of the MNIST data set. In our tests we found that the quantum sampling-based training approach achieves comparable or better accuracy with significantly fewer iterations of generative training than conventional CD-based training. Further investigation is needed to determine whether similar improvements can be achieved for other data sets, and to what extent these improvements can be attributed to quantum effects.