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Benchmarking Adiabatic Quantum Optimization for Complex Network Analysis SANDIA REPORT SAND2015-3025 Unlimited Release June 2015 Benchmarking Adiabatic Quantum Optimization for Complex Network Analysis Ojas Parekh, Jeremy Wendt, Luke Shulenburger, Andrew Landahl, Jonathan Moussa, John Aidun Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. Approved for public release; further dissemination unlimited. 1 Issued by Sandia National Laboratories, operated for the United States Department of Energy by Sandia Corporation. NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors. Printed in the United States of America. This report has been reproduced directly from the best available copy. Available to DOE and DOE contractors from U.S. Department of Energy Office of Scientific and Technical Information P.O. Box 62 Oak Ridge, TN 37831 Telephone: (865) 576-2087 Facsimile: (865) 576-5728 E-Mail: [email protected] Online ordering: http://www.osti.gov/bridge Available to the public from U.S. Department of Commerce National Technical Information Service 5301 Shawnee Rd Alexandria, VA 22312 Telephone: (800) 553-6847 Facsimile: (703) 605-6900 E-Mail: [email protected] Online order: http://www.ntis.gov/help/ordermethods.aspx#online 2 SAND2015-3025 Unlimited Release June 2015 Benchmarking Adiabatic Quantum Optimization for Complex Network Analysis Ojas Parekh Discrete Math & Optimization Center for Computing Research Jeremy Wendt Embedded Systems Engineering Luke Shulenburger HEDP Theory Andrew Landahl, Jonathan Moussa, John Aidun Advanced Device Technologies Center for Computing Research Sandia National Laboratories P.O. Box 5800 Albuquerque, New Mexico 87185-1326 Abstract We lay the foundation for a benchmarking methodology for assessing current and future quantum computers. We pose and begin addressing fundamental questions about how to fairly compare computational devices at vastly different stages of technological maturity. We critically evaluate and offer our own contributions to current quantum benchmarking efforts, in particular those involving adiabatic quantum computation and the Adiabatic Quantum Optimizers produced by D-Wave Systems, Inc. We find that the performance of D-Wave’s Adiabatic Quantum Optimizers scales roughly on par with classical approaches for some hard combinatorial optimization problems; however, architectural limitations of D-Wave devices present a significant hurdle in evaluating real-world applications. In addition to identifying and isolating such limitations, we develop algorithmic tools for circumventing these limitations on future D-Wave devices, assuming they continue to grow and mature at an exponential rate for the next several years. 3 ACKNOWLEDGMENTS Access and computer time on the D-Wave machine located at NASA Ames Research Center were provided by the NASA Ames Research Center and the Universities Space Research Association. 4 Contents Executive Summary ................................................................................................................................ 11 1 Introduction to quantum computing ............................................................................................... 17 1.1 The quantum circuit architecture ............................................................................................................................................................ 17 1.2 The adiabatic quantum architecture ...................................................................................................................................................... 18 1.3 The adiabatic quantum optimization architecture .......................................................................................................................... 18 2 The D-Wave quantum annealer ...................................................................................................... 23 2.1 Solving combinatorial optimization problems on a D-Wave device .......................................................................................... 24 3 Benchmarking methodology ............................................................................................................ 27 3.1 Benchmarking challenges ........................................................................................................................................................................... 27 3.2 Our goals and contribution ......................................................................................................................................................................... 28 3.3 Subtleties in D-Wave benchmarking ....................................................................................................................................................... 29 3.3.1 What is an appropriate measure of success? .......................................................................................................................... 29 3.3.2 Which classical algorithms ought to be used for comparison? ....................................................................................... 30 3.3.3 How does one select appropriate benchmarking instances? .......................................................................................... 32 3.3.4 How large are hard instances? ...................................................................................................................................................... 34 4 Complex-network instance families ................................................................................................ 37 4.1 Introduction ...................................................................................................................................................................................................... 37 4.2 Real-world instances ..................................................................................................................................................................................... 39 4.2.1 Twitter graphs ...................................................................................................................................................................................... 39 4.3 D-Wave-embeddable graphs ...................................................................................................................................................................... 41 4.3.1 D-Wave graph embeddings............................................................................................................................................................. 41 4.3.2 Real-world-like Chimera-minor graphs .................................................................................................................................... 43 5 Quantum benchmarking studies ..................................................................................................... 47 5.1 Introduction ...................................................................................................................................................................................................... 47 5.1.1 Quantum Monte Carlo simulator .................................................................................................................................................. 48 5.2 Chimera Ising spin glass instances........................................................................................................................................................... 49 5.2.1 Methodology .......................................................................................................................................................................................... 49 5.2.2 D-Wave run-time estimation ......................................................................................................................................................... 50 5.2.3 Results ...................................................................................................................................................................................................... 51 5.3 Independent set problems ........................................................................................................................................................................... 53 5.3.1 Problem motivation
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