Function smoothing regularization for precision factorization machine annealing in continuous variable optimization problems
Solving continuous variable optimization problems by factorization machine quantum annealing (FMQA) demonstrates the potential of Ising machines to be extended as a solver for integer and real optimization problems. However, the details of the Hamiltonian function surface obtained by the factorizati...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-02-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.013149 |
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| _version_ | 1823858067550240768 |
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| author | Katsuhiro Endo Kazuaki Z. Takahashi |
| author_facet | Katsuhiro Endo Kazuaki Z. Takahashi |
| author_sort | Katsuhiro Endo |
| collection | DOAJ |
| description | Solving continuous variable optimization problems by factorization machine quantum annealing (FMQA) demonstrates the potential of Ising machines to be extended as a solver for integer and real optimization problems. However, the details of the Hamiltonian function surface obtained by the factorization machine (FM) have been overlooked. This study shows that in the widely used case where real numbers are represented by a combination of binary variables, the function surface of the Hamiltonian obtained by FM can be very noisy. This noise interferes with the inherent capabilities of quantum annealing and is likely to be a substantial cause of problems previously considered unsolvable because of the limitations of FMQA performance. The origin of the noise is identified and a simple, general method is proposed to prevent its occurrence. The generalization performance of the proposed method and its ability to solve practical problems is demonstrated. |
| format | Article |
| id | doaj-art-9f450a5d96844790a3b1a89f75e9c111 |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-9f450a5d96844790a3b1a89f75e9c1112025-02-11T15:08:00ZengAmerican Physical SocietyPhysical Review Research2643-15642025-02-017101314910.1103/PhysRevResearch.7.013149Function smoothing regularization for precision factorization machine annealing in continuous variable optimization problemsKatsuhiro EndoKazuaki Z. TakahashiSolving continuous variable optimization problems by factorization machine quantum annealing (FMQA) demonstrates the potential of Ising machines to be extended as a solver for integer and real optimization problems. However, the details of the Hamiltonian function surface obtained by the factorization machine (FM) have been overlooked. This study shows that in the widely used case where real numbers are represented by a combination of binary variables, the function surface of the Hamiltonian obtained by FM can be very noisy. This noise interferes with the inherent capabilities of quantum annealing and is likely to be a substantial cause of problems previously considered unsolvable because of the limitations of FMQA performance. The origin of the noise is identified and a simple, general method is proposed to prevent its occurrence. The generalization performance of the proposed method and its ability to solve practical problems is demonstrated.http://doi.org/10.1103/PhysRevResearch.7.013149 |
| spellingShingle | Katsuhiro Endo Kazuaki Z. Takahashi Function smoothing regularization for precision factorization machine annealing in continuous variable optimization problems Physical Review Research |
| title | Function smoothing regularization for precision factorization machine annealing in continuous variable optimization problems |
| title_full | Function smoothing regularization for precision factorization machine annealing in continuous variable optimization problems |
| title_fullStr | Function smoothing regularization for precision factorization machine annealing in continuous variable optimization problems |
| title_full_unstemmed | Function smoothing regularization for precision factorization machine annealing in continuous variable optimization problems |
| title_short | Function smoothing regularization for precision factorization machine annealing in continuous variable optimization problems |
| title_sort | function smoothing regularization for precision factorization machine annealing in continuous variable optimization problems |
| url | http://doi.org/10.1103/PhysRevResearch.7.013149 |
| work_keys_str_mv | AT katsuhiroendo functionsmoothingregularizationforprecisionfactorizationmachineannealingincontinuousvariableoptimizationproblems AT kazuakiztakahashi functionsmoothingregularizationforprecisionfactorizationmachineannealingincontinuousvariableoptimizationproblems |