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Quantum Speedup for Aeroscience and Engineering NASA/TM-2020-220590 Quantum Speedup for Aeroscience and Engineering Peyman Givi University of Pittsburgh, Pittsburgh, Pennsylvania Andrew J. Daley University of Strathclyde, Glasgow, United Kingdom Dimitri Mavriplis University of Wyoming, Laramie, Wyoming Mujeeb Malik Langley Research Center, Hampton, Virginia May 2020 NASA STI Program . in Profile Since its founding, NASA has been dedicated to • CONFERENCE PUBLICATION. Collected the advancement of aeronautics and space science. papers from scientific and technical The NASA scientific and technical information conferences, symposia, seminars, or other (STI) program plays a key part in helping NASA meetings sponsored or co-sponsored by maintain this important role. NASA. The NASA STI program operates under the • SPECIAL PUBLICATION. Scientific, auspices of the Agency Chief Information Officer. It technical, or historical information from collects, organizes, provides for archiving, and NASA programs, projects, and missions, often disseminates NASA’s STI. The NASA STI program concerned with subjects having substantial provides access to the NASA Aeronautics and Space public interest. Database and its public interface, the NASA Technical Report Server, thus providing one of the • TECHNICAL TRANSLATION. English- largest collections of aeronautical and space science language translations of foreign scientific and STI in the world. Results are published in both non- technical material pertinent to NASA’s NASA channels and by NASA in the NASA STI mission. Report Series, which includes the following report types: Specialized services also include creating custom thesauri, building customized databases, • TECHNICAL PUBLICATION. Reports of and organizing and publishing research results. completed research or a major significant phase of research that present the results of For more information about the NASA STI NASA programs and include extensive data or program, see the following: theoretical analysis. Includes compilations of significant scientific and technical data and • Access the NASA STI program home page at information deemed to be of continuing http://www.sti.nasa.gov reference value. NASA counterpart of peer- reviewed formal professional papers, but • E-mail your question via the Internet to having less stringent limitations on manuscript [email protected] length and extent of graphic presentations. • Fax your question to the NASA STI Help Desk • TECHNICAL MEMORANDUM. Scientific at 443-757-5803 and technical findings that are preliminary or of specialized interest, e.g., quick release • Phone the NASA STI Help Desk at reports, working papers, and bibliographies 443-757-5802 that contain minimal annotation. Does not contain extensive analysis. • Write to: NASA STI Help Desk • CONTRACTOR REPORT. Scientific and NASA Center for AeroSpace Information technical findings by NASA-sponsored 7115 Standard Drive contractors and grantees. Hanover, MD 21076-1320 NASA/TM-2020-220590 Quantum Speedup for Aeroscience and Engineering Peyman Givi University of Pittsburgh, Pittsburgh, Pennsylvania Andrew J. Daley University of Strathclyde, Glasgow, United Kingdom Dimitri Mavriplis University of Wyoming, Laramie, Wyoming Mujeeb Malik Langley Research Center, Hampton, Virginia National Aeronautics and Space Administration Langley Research Center Hampton, Virginia 23681-2199 May 2020 The use of trademarks or names of manufacturers in this report is for accurate reporting and does not constitute an official endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics and Space Administration. Available from: NASA Center for AeroSpace Information 7115 Standard Drive Hanover, MD 21076-1320 443-757-5802 Abstract Algorithms and hardware for quantum computing (QC) are reaching a critical stage in their development and have the potential to generate a paradigm shift in computing capability across a range of fields. Opportunities are growing for genuine impact of these systems over a timescale of 10-15 years, and there has been significant investment both from government agencies and private industry in its development. However, utilization of quantum phenomena is extraordinarily challenging due to its delicate nature and difficulties in measurement and control. A clear path exists toward demonstrating the advantages of QC over existing high- performance computing for some physics and materials science problems but addressing practical computational challenges in other fields, though promising, is at an early stage of development. Reaching the next level of development will require strategic coordination between physicists, computer & information scientists, mathematicians, and engineers, in order to transition this technology from the laboratory to robust and scalable computations for practical problems, especially those of interest to the aeroscience and engineering community. This community has been relying on high-performance computing heavily and will surely want to be informed of the developments in QC. This survey introduces the background and current state of the art in QC, as well as its perceived opportunities and challenges. v Table of Contents 1. Introduction ................................................................................................................................. 1 1.1. Background .......................................................................................................................... 1 1.2. Investment in QC ................................................................................................................. 2 1.3. Opportunities for Aeroscience Applications ........................................................................ 3 1.4. Purpose and Structure of This Survey .................................................................................. 3 2. Universal Quantum Computing and Quantum Speedup ............................................................. 4 3. Implementation of Digital Quantum Computing ........................................................................ 6 3.1. Decoherence and Error Correction ....................................................................................... 6 3.2. Hardware for Universal Quantum Computing ..................................................................... 7 4. Alternatives to Gate-Based Digital Quantum Computing ........................................................ 10 5. QC Prospects for Aeroscience and Engineering ....................................................................... 12 5.1. Linear Equations and Machine Learning ........................................................................... 13 5.2. Differential Equations ........................................................................................................ 13 5.3. Current QC Communities ................................................................................................... 14 6. Future Prospects ........................................................................................................................ 15 Acknowledgments......................................................................................................................... 18 References ..................................................................................................................................... 19 Figures........................................................................................................................................... 28 vi 1. Introduction Moore’s law [1] has largely held true for over five decades. However, over the last few years, there has been increasing discussion about its continued longevity as illustrated in figure 1 [2]. As silicon processes shrink to smaller and smaller sizes, physical limitations start to play an important role. As a result, the expense and effort required to continue the increase in performance are now much greater than ever before. In order to provide new disruptive means to perform computations with increased complexity, high-performance computing will need a radical departure from the conventional classical computing platform. Quantum computing (QC), which makes use of the unusual physical properties of microscopic objects to process information, is a particularly promising candidate to be this disruptive technology for a range of computational problems [3– 12]. 1.1. Background Quantum Computing is one branch of the more general fields of Quantum Information Science (QIS) and Quantum Technology. QIS represents the merger of the two most significant scientific and technological revolutions of the 20th century notably quantum physics and information technology. The resulting devices have the potential to revolutionize applications in sensing and metrology, communication, simulation, and computing. Realization of the enormous scientific, economic, and security implications of quantum technologies has led to rapidly growing investment worldwide, both from national governments in the U.S. and abroad, and from private enterprises, as we detail below. Quantum computing as an area has undergone rapid development both in hardware and software over the last decade. Used in appropriate ways, quantum mechanics can provide powerful resources for solving certain classes of problems, achieving cost scalings with the size of the problem that are not achievable with existing “classical” computers [10, 13]. This is known as “quantum speedup.” Amongst the oldest and best known examples
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