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A recent Google study [Phys. Rev. X, 6:031015 (2016)] compared a D-Wave 2X quantum processing unit (QPU) to two classical Monte Carlo algorithms: simulated annealing (SA) and quantum Monte Carlo (QMC). The study showed the D-Wave 2X to be up to 100 million times faster than the classical algorithms. The Google inputs are designed to demonstrate the value of collective multiqubit tunneling, a resource that is available to D-Wave QPUs but not to simulated annealing. But the computational hardness in these inputs is highly localized in gadgets, with only a small amount of complexity coming from global interactions, meaning that the relevance to real-world problems is limited.In this study we provide a new synthetic problem class that addresses the limitations of the Google inputs while retaining their strengths. We use simple clusters instead of more complex gadgets and more emphasis is placed on creating computational hardness through frustrated global interactions like those seen in interesting real-world inputs. The logical spin-glass backbones used to generate these inputs are planar Ising models without fields and the problems can therefore be solved in polynomial time [J. Phys. A, 15:10 (1982)]. However, for general heuristic algorithms that are unaware of the planted problem class, the frustration creates meaningful difficulty in a controlled environment ideal for study.We use these inputs to evaluate the new 2000-qubit D-Wave QPU. We include the HFS algorithm-the best performer in a broader analysis of Google inputs-and we include state-ofthe-art GPU implementations of SA and QMC. The D-Wave QPU solidly outperforms the software solvers: when we consider pure annealing time (computation time), the D-Wave QPU reaches ground states up to 2600 times faster than the competition. In the task of zero-temperature Boltzmann sampling from challenging multimodal inputs, the D-Wave QPU holds a similar advantage and does not see significant performance degradation due to quantum sampling bias. CONTENTS

This paper describes an experimental study of a novel computing system (algorithm plus platform) that carries out quantum annealing, a type of adiabatic quantum computation, to solve optimization problems. We compare this system to three conventional software solvers, using instances from three NP-hard problem domains. We also describe experiments to learn how performance of the quantum annealing algorithm depends on input.

The performance of sequential search can be enhanced by the use of heuristics that move elements closer to the front of the list as they are found. Previous analyses have characterized the performance of such heuristics probabilistically. In this article,, we use amortization to analyze the heuristics in a worst-case sense; the relative merit of the heuristics in this analysis is different in the probabilistic analyses. Experiments show that the behavior of the heuristics on real data is more closely described by the amortized analyses than by the probabilistic analyses.404

Computational experiments on algorithms can supplement theoretical analysis by showing what algorithms, implementations and speed-up methods work best for specific machines or problems. This book guides the reader through the nuts and bolts of the major experimental questions: What should I measure? What inputs should I test? How do I analyze the data? To answer these questions the book draws on ideas from algorithm design and analysis, computer systems, and statistics and data analysis. The wide-ranging discussion includes a tutorial on system clocks and CPU timers, a survey of strategies for tuning algorithms and data structures, a cookbook of methods for generating random combinatorial inputs, and a demonstration of variance reduction techniques. The book can be used by anyone who has taken a course or two in data structures and algorithms. A companion website, AlgLab (www.cs.amherst.edu/alglab) contains downloadable files, programs and tools for use in experimental projects.

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Please scroll down for article-it is on subsequent pages With 12,500 members from nearly 90 countries, INFORMS is the largest international association of operations research (O.R.) and analytics professionals and students. INFORMS provides unique networking and learning opportunities for individual professionals, and organizations of all types and sizes, to better understand and use O.R. and analytics tools and methods to transform strategic visions and achieve better outcomes. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org

A central goal in quantum computing is the development of quantum hardware and quantum algorithms in order to analyse challenging scientific and engineering problems. Research in quantum computation involves contributions from both physics and computer science, hence this article presents a concise introduction to basic concepts from both fields that are used in annealing-based quantum computation, an alternative to the more familiar quantum gate model.We introduce some concepts from computer science required to define difficult computational problems and to realise the potential relevance of quantum algorithms to find novel solutions to those problems. We introduce the structure of quantum annealing-based algorithms as well as two examples of this kind of algorithms for solving instances of the max-SAT and Minimum Multicut problems. An overview of the quantum annealing systems manufactured by D-Wave Systems is also presented.Quantum annealing is a physical platform of quantum computation focused on solving combinatorial optimisation problems. Quantum annealing is a restricted form of adiabatic quantum computation but the problems that can be explored using this paradigm are vast and relevant to many fields of science and technology. D-Wave systems manufactures commercially available quantum annealingbased hardware on which it is possible to run algorithms. Thanks to the access granted by USRA-NASA to the D-Wave's quantum annealer installed at NASA Ames Research Centre, our work on quantum annealing-based algorithms and the examples presented in this paper have been designed, tested and run using both D-Wave's quantum annealer and D-Wave's advanced simulation software. Future quantum annealers probably will use similar hardware and programming principles as D-Wave's, so we expect that our discussions and results will have a broad impact in the field of annealingbased quantum computation.