D-Wave quantum annealers represent a novel computational architecture and have attracted significant interest. Much of this interest has focused on the quantum behavior of D-Wave machines, and there have been few practical algorithms that use the D-Wave. Machine learning has been identified as an area where quantum annealing may be useful. Here, we show that the D-Wave 2X can be effectively used as part of an unsupervised machine learning method. This method takes a matrix as input and produces two low-rank matrices as output—one containing latent features in the data and another matrix describing how the features can be combined to approximately reproduce the input matrix. Despite the limited number of bits in the D-Wave hardware, this method is capable of handling a large input matrix. The D-Wave only limits the rank of the two output matrices. We apply this method to learn the features from a set of facial images and compare the performance of the D-Wave to two classical tools. This method is able to learn facial features and accurately reproduce the set of facial images. The performance of the D-Wave shows some promise, but has some limitations. It outperforms the two classical codes in a benchmark when only a short amount of computational time is allowed (200-20,000 microseconds), but these results suggest heuristics that would likely outperform the D-Wave in this benchmark.

Despite the impact that hydraulic fracturing has had on the energy sector, the physical mechanisms that control its efficiency and environmental impacts remain poorly understood in part because the length scales involved range from nanometres to kilometres. We characterize flow and transport in shale formations across and between these scales using integrated computational, theoretical and experimental efforts/methods. At the field scale, we use discrete fracture network modelling to simulate production of a hydraulically fractured well from a fracture network that is based on the site characterization of a shale gas reservoir. At the core scale, we use triaxial fracture experiments and a finite-discrete element model to study dynamic fracture/crack propagation in low permeability shale. We use lattice Boltzmann pore-scale simulations and microfluidic experiments in both synthetic and shale rock micromodels to study pore-scale flow and transport phenomena, including multi-phase flow and fluids mixing. A mechanistic description and integration of these multiple scales is required for accurate predictions of production and the eventual optimization of hydrocarbon extraction from unconventional reservoirs. Finally, we discuss the potential of CO2 as an alternative working fluid, both in fracturing and re-stimulating activities, beyond its environmental advantages.This article is part of the themed issue 'Energy and the subsurface'.

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Climate change and thawing permafrost in the arctic will significantly alter landscape hydro-geomorphology and the distribution of soil moisture, which will have cascading effects on climate feedbacks (CO2 and CH4), and plant and microbial communities. Fundamental processes critical to predicting active layer hydrology are not well understood. This study applied water stable isotope techniques ( 2 H and  18 O) to infer sources and mixing of active layer waters in a polygonal tundra landscape in Barrow, Alaska (USA) in August and September of 2012. Results suggested that winter precipitation did not contribute substantially to surface waters or subsurface active layer pore waters measured in August and September. Summer rain was the main source of water to the active layer, with seasonal ice-melt contributing to deeper pore waters later in the season. Surface water evaporation was evident in August from a characteristic isotopic fractionation slope ( 2 H versus  18 O). Freeze-out isotopic fractionation effects in frozen active layer samples and textural permafrost were indistinguishable from evaporation fractionation, emphasizing the importance of considering the most likely processes in water isotope studies, in systems where both evaporation and freeze-out occur in close proximity. The fractionation observed in frozen active layer ice was not observed in liquid active layer pore waters. Such a discrepancy between frozen and liquid active layer samples suggests mixing of melt water, likely due to slow melting of seasonal ice. This research provides insight into fundamental processes relating to sources and mixing of active layer waters, which should be considered in process-based fine and intermediate scale hydrologic models.

Variance-based sensitivity analysis provides a quantitative measure of how uncertainty in a model input contributes to uncertainty in the model output. Such sensitivity analyses arise in a wide variety of applications and are typically computed using Monte Carlo estimation, but the many samples required for Monte Carlo to be sufficiently accurate can make these analyses intractable when the model is expensive. This work presents a multifidelity approach for estimating sensitivity indices that leverages cheaper low-fidelity models to reduce the cost of sensitivity analysis while retaining accuracy guarantees via recourse to the original, expensive model. This paper develops new multifidelity estimators for variance and for the Sobol' main and total effect sensitivity indices. We discuss strategies for dividing limited computational resources among models and specify a recommended strategy. Results are presented for the Ishigami function and a convection-diffusionreaction model that demonstrate up to 10× speedups for fixed convergence levels. For the problems tested, the multifidelity approach allows inputs to be definitively ranked in importance when Monte Carlo alone fails to do so.

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It was recently shown that quantum annealing can be used as an effective, fast subroutine in certain types of matrix factorization algorithms. The quantum annealing algorithm performed best for quick, approximate answers, but performance rapidly plateaued. In this paper, we utilize reverse annealing instead of forward annealing in the quantum annealing subroutine for nonnegative/binary matrix factorization problems. After an initial global search with forward annealing, reverse annealing performs a series of local searches that refine existing solutions. The combination of forward and reverse annealing significantly improves performance compared to forward annealing alone for all but the shortest run times.

Abstract-Quantum computers are becoming more widely available, so it is important to develop tools that enable people to easily program these computers to solve complex problems. To address this issue, we present the design and two applications of ToQ.jl, a high-level programming language for D-Wave quantum annealing machines. ToQ.jl leverages the metaprogramming facilities in Julia (a high-level, high-performance programming language tor technical computing) and uses D-Wave's ToQ programming language as an intermediate representation. This makes it possible for a programmer to leverage all the capabilities of Julia, and the D-Wave machine is used as a co-processor. We demonstrate ToQ.jl via two applications: (1) a pedagogical example based on a map-coloring problem and (2) a linear least squares problem. We also discuss our experience using ToQ.jl with a D-Wave 2X, particularly with respect to a linear least squares problem which is 01' broad interest to the scientific computing community.