Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models

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.Comment: 17 pages, 8 figures. Minor further revisions. As published in Phys. Rev.

Label-driven weakly-supervised learning for multimodal deformable image registration

Spatially aligning medical images from different modalities remains a challenging task, especially for intraoperative applications that require fast and robust algorithms. We propose a weakly-supervised, label-driven formulation for learning 3D voxel correspondence from higher-level label correspondence, thereby bypassing classical intensity-based image similarity measures. During training, a convolutional neural network is optimised by outputting a dense displacement field (DDF) that warps a set of available anatomical labels from the moving image to match their corresponding counterparts in the fixed image. These label pairs, including solid organs, ducts, vessels, point landmarks and other ad hoc structures, are only required at training time and can be spatially aligned by minimising a cross-entropy function of the warped moving label and the fixed label. During inference, the trained network takes a new image pair to predict an optimal DDF, resulting in a fully-automatic, label-free, real-time and deformable registration. For interventional applications where large global transformation prevails, we also propose a neural network architecture to jointly optimise the global- and local displacements. Experiment results are presented based on cross-validating registrations of 111 pairs of T2-weighted magnetic resonance images and 3D transrectal ultrasound images from prostate cancer patients with a total of over 4000 anatomical labels, yielding a median target registration error of 4.2 mm on landmark centroids and a median Dice of 0.88 on prostate glands.Comment: Accepted to ISBI 201

A generative modeling approach for benchmarking and training shallow quantum circuits

Hybrid quantum-classical algorithms provide ways to use noisy intermediate-scale quantum computers for practical applications. Expanding the portfolio of such techniques, we propose a quantum circuit learning algorithm that can be used to assist the characterization of quantum devices and to train shallow circuits for generative tasks. The procedure leverages quantum hardware capabilities to its fullest extent by using native gates and their qubit connectivity. We demonstrate that our approach can learn an optimal preparation of the Greenberger-Horne-Zeilinger states, also known as "cat states". We further demonstrate that our approach can efficiently prepare approximate representations of coherent thermal states, wave functions that encode Boltzmann probabilities in their amplitudes. Finally, complementing proposals to characterize the power or usefulness of near-term quantum devices, such as IBM's quantum volume, we provide a new hardware-independent metric called the qBAS score. It is based on the performance yield in a specific sampling task on one of the canonical machine learning data sets known as Bars and Stripes. We show how entanglement is a key ingredient in encoding the patterns of this data set; an ideal benchmark for testing hardware starting at four qubits and up. We provide experimental results and evaluation of this metric to probe the trade off between several architectural circuit designs and circuit depths on an ion-trap quantum computer.Comment: 16 pages, 9 figures. Minor revisions. As published in npj Quantum Informatio