Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of within-thecluster distances between points. The straightforward approach involves examining all the possible assignments of points to each of the clusters. This approach guarantees the solution will be a global minimum, however the number of possible assignments scales quickly with the number of data points and becomes computationally intractable even for very small datasets. In order to circumvent this issue, cost function minima are found using popular local-search based heuristic approaches such as k-means and hierarchical clustering. Due to their greedy nature, such techniques do not guarantee that a global minimum will be found and can lead to sub-optimal clustering assignments. Other classes of global-search based techniques, such as simulated annealing, tabu search, and genetic algorithms may offer better quality results but can be too time consuming to implement. In this work, we describe how quantum annealing can be used to carry out clustering. We map the clustering objective to a quadratic binary optimization (QUBO) problem and discuss two clustering algorithms which are then implemented on commercially-available quantum annealing hardware, as well as on a purely classical solver "qbsolv." The first algorithm assigns N data points to K clusters, and the second one can be used to perform binary clustering in a hierarchical manner. We present our results in the form of benchmarks against well-known k-means clustering and discuss the advantages and disadvantages of the proposed techniques.
NP-hard optimization problems scale very rapidly with problem size, becoming unsolvable with brute force methods, even with supercomputing resources. Typically, such problems have been approximated with heuristics. However, these methods still take a long time and are not guaranteed to find an optimal solution. Quantum computing offers the possibility of producing significant speed-up and improved solution quality. Current quantum annealing (QA) devices are designed to solve difficult optimization problems, but they are limited by hardware size and qubit connectivity restrictions. We present a novel heterogeneous computing stack that combines QA and classical machine learning, allowing the use of QA on problems larger than the hardware limits of the quantum device. These results represent experiments on a real-world problem represented by the weighted k-clique problem. Through this experiment, we provide insight into the state of quantum machine learning.
Although quantum computing hardware has evolved significantly in recent years, spurred by increasing industrial and government interest, the size limitation of current generation quantum computers remains an obstacle when applying these devices to relevant, real-world problems. In order to effectively exploit the potential benefits of quantum computing, heterogeneous approaches that combine both classical and quantum computing techniques are needed. In this work, we explore multiple heterogeneous approaches to solving multiple industry-relevant benchmark problems in order to understand how best to leverage quantum computers given current constraints. Our results indicate: that solver performance is highly dependent on the structure (size and edge density) of the problem graph; that reusing a single fixed problem embedding, as opposed to dynamically searching for problem embeddings, is key to avoiding computational bottlenecks; that solutions of better quality are produced by algorithms that iteratively propagate the influence that solving an individual sub-problem has to the remainder of the larger problem; and that the Qbsolv algorithm (which implements the aforementioned techniques) is, at this time, the stateof-the-art in producing quality solutions, in a timely fashion, to a variety of theoretical and real-world problems too large to directly embed onto a quantum annealing device.
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