“Probabilistic models with discrete latent variables naturally capture datasets composed of discrete classes. However, they are difficult to train efficiently, since back propagation through discrete variables is generally not possible. We introduce a novel class of probabilistic models, comprising an undirected discrete component and a directed hierarchical continuous component, that can be trained efficiently using the variational autoencoder framework. The discrete component captures the distribution over the disconnected smooth manifolds induced by the continuous component. As a result, this class of models efficiently learns both the class of objects in an image, and their specific realization in pixels, from unsupervised data; and outperforms state-of-the-art methods on the permutation-invariant MNIST, OMNIGLOT, and Caltech-101 Silhouettes datasets.”

(7 Sep 2016) http://arxiv.org/abs/1609.02200

Zhengbing Bian, Fabian Chudak, Robert Israel, Brad Lackey, William G. Macready, Aidan Roy

Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions, and propose two new decomposition algorithms for solving problems too large to map directly into hardware.

(10 Mar 2016) http://arxiv.org/abs/1603.03111

Tomas Boothby, Andrew D. King, Aidan Roy

(27 Oct 2015) http://link.springer.com/article/10.1007/s11128-015-1150-6?wt_mc=internal.event.1.SEM.ArticleAuthorOnlineFirst

A.D.King, T.Lanting, and R.Harris

(3 Sep 2015) http://arxiv.org/pdf/1502.02098.pdf

Mohammad H. Amin

(13 Mar 2015) http://arxiv.org/pdf/1503.04216.pdf

Jun Cai, Bill Macready, Aidan Roy

(12 Jun 2014) http://arxiv.org/pdf/1406.2741.pdf

N G Dickson et al. 

"Efforts to develop useful quantum computers have been blocked primarily by environmental noiseHere we examine the environment’s effect on quantum annealing using 16 qubits of a superconducting quantum processor. For a problem instance with an isolated small-gap anticrossing between the lowest two energy levels, we experimentally demonstrate that, even with annealing times eight orders of magnitude longer than the predicted single-qubit decoherence time, the probabilities of performing a successful computation are similar to those expected for a fully coherent system. Moreover, for the problem studied, we show that quantum annealing can take advantage of a thermal environment to achieve a speedup factor of up to 1,000 over a closed system."

Nature Communications, 1903 (May 21 2013) http://www.nature.com/ncomms/journal/v4/n5/full/ncomms2920.html

M. W. Johnson et al. 

Many interesting but practically intractable problems can be reduced to that of finding the ground state of a system of interacting spins; however, finding such a ground state remains computationally difficult..Here we use quantum annealing to find the ground state of an artificial Ising spin system comprising an array of eight superconducting flux quantum bits with programmable spin–spin couplings. We observe a clear signature of quantum annealing, distinguishable from classical thermal annealing through the temperature dependence of the time at which the system dynamics freezes.

Nature 473, 194-198 (12 May 2011) http://www.nature.com/nature/journal/v473/n7346/full/nature10012.html

Z. Bian et al. 
Link to PDF

R. Harris et al.
Physical Review B 81, 134510 (2010) arXiv:0909.4321

F. Hamze et al
International Journal of Modern Physics C, Volume 21, issue 5 (2010) arXiv:1004.2840

T. Lanting et al.
Phys. Rev. B 82, 060512(R) (2010) arXiv:1006.0028

Phys. Rev. Lett. 102, 220401 (2009) arXiv:0810.4335

M. H. S. Amin et al.
Phys. Rev. A 80, 062326 (2009) arXiv:0904.1387