D-Wave Quantum

K. Boothby, P. Bunyk, Jack Raymond, Aidan Roy

This paper presents an overview of the topology of D-Wave's next-generation quantum processors. It provides examples of minor embeddings and discusses performance of embedding algorithms for the new topology compared to the existing Chimera topology. It also presents some initial performance results for simple, standard Ising model classes of problems.

Dennis Willsch, M. Willsch, H. De Raedt, K. Michielsen

Kernel-based support vector machines (SVMs) are supervised machine learning algorithms for classification and regression problems. We present a method to train SVMs on a D-Wave 2000Q quantum annealer and study its performance in comparison to SVMs trained on conventional computers. The method is applied to both synthetic data and real data obtained from biology experiments. We find that the quantum annealer produces an ensemble of different solutions that often generalizes better to unseen data than the single global minimum of an SVM trained on a conventional computer, especially in cases where only limited training data is available. For cases with more training data than currently fits on the quantum annealer, we show that a combination of classifiers for subsets of the data almost always produces stronger joint classifiers than the conventional SVM for the same parameters.

K. Boothby, A. King

Costantino Carugno, Maurizio Ferrari Dacrema, P. Cremonesi

Job Shop Scheduling is a combinatorial optimization problem of particular importance for production environments where the goal is to complete a production task in the shortest possible time given limitations in the resources available. Due to its computational complexity it quickly becomes intractable for problems of interesting size. The emerging technology of Quantum Annealing provides an alternative computational architecture that promises improved scalability and solution quality. However, several limitations as well as open research questions exist in this relatively new and rapidly developing technology. This paper studies the application of quantum annealing to solve the job shop scheduling problem, describing each step required from the problem formulation to the fine-tuning of the quantum annealer and compares the solution quality with various classical solvers. Particular attention is devoted to aspects that are often overlooked, such as the computational cost of representing the problem in the formulation required by the quantum annealer, the relative qubits requirements and how to mitigate chain breaks. Furthermore, the impact of advanced tools such as reverse annealing is presented and its effectiveness discussed. The results indicate several challenges emerging at various stages of the experimental pipeline which bring forward important research questions and directions of improvement.

Elijah Pelofske

Quantum annealing (QA) is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. QA in the transverse Ising model, implemented on D-Wave quantum processing units, are available as cloud computing resources. In this study we report concise benchmarks across three generations of D-Wave quantum annealers, consisting of four different devices, for the NP-hard discrete combinatorial optimization problems unweighted maximum clique and unweighted maximum cut on random graphs. The Ising, or equivalently quadratic unconstrained binary optimization, formulation of these problems do not require auxiliary variables for order reduction, and their overall structure and weights are not highly variable, which makes these problems simple test cases to understand the sampling capability of current D-Wave quantum annealers. All-to-all minor embeddings of size 52, with relatively uniform chain lengths, are used for a direct comparison across the Chimera, Pegasus, and Zephyr device topologies. A grid-search over annealing times and the minor embedding chain strengths is performed in order to determine the level of reasonable performance for each device and problem type. Experiment metrics that are reported are approximation ratios for non-broken chain samples, chain break proportions, and time-to-solution for the maximum clique problem instances. How fairly the quantum annealers sample optimal maximum cliques, for instances which contain multiple maximum cliques, is quantified using entropy of the measured ground state distributions. The newest generation of quantum annealing hardware, which has a Zephyr hardware connectivity, performed the best overall with respect to approximation ratios and chain break frequencies.