Singleton, RL and Rogers, ML (2020) Floating-Point Calculations on a Quantum Annealer: Division and Matrix Inversion. Frontiers in Physics, 8. 265. ISSN 2296-424X
Abstract
Systems of linear equations are employed almost universally across a wide range of disciplines, from physics and engineering to biology, chemistry, and statistics. Traditional solution methods such as Gaussian elimination are very time consuming for large matrices, and more efficient computational methods are desired. In the twilight of Moore's Law, quantum computing is perhaps the most direct path out of the darkness. There are two complementary paradigms for quantum computing, namely, circuit-based systems and quantum annealers. In this paper, we express floating point operations, such as division and matrix inversion, in terms of a quadratic unconstrained binary optimization (QUBO) problem, a formulation that is ideal for a quantum annealer. We first address floating point division, and then move on to matrix inversion. We provide a general algorithm for any number of dimensions, and, as a proof-of-principle, we demonstrates results from the D-Wave quantum annealer for 2 × 2 and 3 × 3 general matrices. In principle, our algorithm scales to very large numbers of linear equations; however, in practice the number is limited by the connectivity and dynamic range of the machine.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 Rogers and Singleton. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. |
Keywords: | quantum computing, matrix inversion, quantum annealing algorithm, linear algebra algorithms, D-wave |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds) > Physics & Astronomy Visitors (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Jun 2020 10:14 |
Last Modified: | 25 Jun 2023 22:19 |
Status: | Published |
Publisher: | Frontiers Media |
Identification Number: | 10.3389/fphy.2020.00265 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:162488 |