Floating-Point Calculations on a Quantum Annealer: Division and Matrix Inversion
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 m...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2020-11-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2020.00265/full |
| _version_ | 1818404111939272704 |
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| author | Michael L. Rogers Robert L. Singleton |
| author_facet | Michael L. Rogers Robert L. Singleton |
| author_sort | Michael L. Rogers |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T08:34:58Z |
| format | Article |
| id | doaj.art-274e10d5e6114c51afe4ac2d3cbb87c1 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-14T08:34:58Z |
| publishDate | 2020-11-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-274e10d5e6114c51afe4ac2d3cbb87c12022-12-21T23:09:25ZengFrontiers Media S.A.Frontiers in Physics2296-424X2020-11-01810.3389/fphy.2020.00265451474Floating-Point Calculations on a Quantum Annealer: Division and Matrix InversionMichael L. Rogers0Robert L. Singleton1SavantX, Santa Fe, NM, United StatesSchool of Mathematics, University of Leeds, Leeds, United KingdomSystems 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.https://www.frontiersin.org/articles/10.3389/fphy.2020.00265/fullquantum computingmatrix inversionquantum annealing algorithmlinear algebra algorithmsD-wave |
| spellingShingle | Michael L. Rogers Robert L. Singleton Floating-Point Calculations on a Quantum Annealer: Division and Matrix Inversion Frontiers in Physics quantum computing matrix inversion quantum annealing algorithm linear algebra algorithms D-wave |
| title | Floating-Point Calculations on a Quantum Annealer: Division and Matrix Inversion |
| title_full | Floating-Point Calculations on a Quantum Annealer: Division and Matrix Inversion |
| title_fullStr | Floating-Point Calculations on a Quantum Annealer: Division and Matrix Inversion |
| title_full_unstemmed | Floating-Point Calculations on a Quantum Annealer: Division and Matrix Inversion |
| title_short | Floating-Point Calculations on a Quantum Annealer: Division and Matrix Inversion |
| title_sort | floating point calculations on a quantum annealer division and matrix inversion |
| topic | quantum computing matrix inversion quantum annealing algorithm linear algebra algorithms D-wave |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2020.00265/full |
| work_keys_str_mv | AT michaellrogers floatingpointcalculationsonaquantumannealerdivisionandmatrixinversion AT robertlsingleton floatingpointcalculationsonaquantumannealerdivisionandmatrixinversion |