Scalable circuit depth reduction in feedback-based quantum optimization with a quadratic approximation
Combinatorial optimization problems are one of the areas where near-term noisy quantum computers may have practical advantage against classical computers. Recently, a feedback-based quantum optimization algorithm has been proposed by Magann et al., Phys. Rev. Lett. 129, 250502 (2022)10.1103/PhysRevL...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.013035 |
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| author | Don Arai Ken N. Okada Yuichiro Nakano Kosuke Mitarai Keisuke Fujii |
| author_facet | Don Arai Ken N. Okada Yuichiro Nakano Kosuke Mitarai Keisuke Fujii |
| author_sort | Don Arai |
| collection | DOAJ |
| description | Combinatorial optimization problems are one of the areas where near-term noisy quantum computers may have practical advantage against classical computers. Recently, a feedback-based quantum optimization algorithm has been proposed by Magann et al., Phys. Rev. Lett. 129, 250502 (2022)10.1103/PhysRevLett.129.250502. The method explicitly determines quantum circuit parameters by feeding back measurement results thus avoids classical parameter optimization that is known to cause significant trouble in quantum approximate optimization algorithm, the well-studied near-term algorithm. Meanwhile, a significant drawback of the feedback-based quantum optimization is that it requires deep circuits, rendering the method unsuitable to noisy quantum devices. In this study we propose a feedback law for parameter determination by introducing the second-order approximation with respect to time interval, a hyperparameter in the feedback-based quantum optimization. This allows one to take larger time interval, leading to acceleration of convergence to solutions. In numerical simulations on the maximum cut problem we demonstrate that our proposal significantly reduces circuit depth, with its linear scaling with the problem size smaller by more than an order of magnitude. We expect that the feedback law proposed in this work may pave the way for feedback-based quantum optimization with near-term noisy quantum computers. |
| format | Article |
| id | doaj-art-8d3868ea222441f6a843f32213de8268 |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-8d3868ea222441f6a843f32213de82682025-01-09T15:04:00ZengAmerican Physical SocietyPhysical Review Research2643-15642025-01-017101303510.1103/PhysRevResearch.7.013035Scalable circuit depth reduction in feedback-based quantum optimization with a quadratic approximationDon AraiKen N. OkadaYuichiro NakanoKosuke MitaraiKeisuke FujiiCombinatorial optimization problems are one of the areas where near-term noisy quantum computers may have practical advantage against classical computers. Recently, a feedback-based quantum optimization algorithm has been proposed by Magann et al., Phys. Rev. Lett. 129, 250502 (2022)10.1103/PhysRevLett.129.250502. The method explicitly determines quantum circuit parameters by feeding back measurement results thus avoids classical parameter optimization that is known to cause significant trouble in quantum approximate optimization algorithm, the well-studied near-term algorithm. Meanwhile, a significant drawback of the feedback-based quantum optimization is that it requires deep circuits, rendering the method unsuitable to noisy quantum devices. In this study we propose a feedback law for parameter determination by introducing the second-order approximation with respect to time interval, a hyperparameter in the feedback-based quantum optimization. This allows one to take larger time interval, leading to acceleration of convergence to solutions. In numerical simulations on the maximum cut problem we demonstrate that our proposal significantly reduces circuit depth, with its linear scaling with the problem size smaller by more than an order of magnitude. We expect that the feedback law proposed in this work may pave the way for feedback-based quantum optimization with near-term noisy quantum computers.http://doi.org/10.1103/PhysRevResearch.7.013035 |
| spellingShingle | Don Arai Ken N. Okada Yuichiro Nakano Kosuke Mitarai Keisuke Fujii Scalable circuit depth reduction in feedback-based quantum optimization with a quadratic approximation Physical Review Research |
| title | Scalable circuit depth reduction in feedback-based quantum optimization with a quadratic approximation |
| title_full | Scalable circuit depth reduction in feedback-based quantum optimization with a quadratic approximation |
| title_fullStr | Scalable circuit depth reduction in feedback-based quantum optimization with a quadratic approximation |
| title_full_unstemmed | Scalable circuit depth reduction in feedback-based quantum optimization with a quadratic approximation |
| title_short | Scalable circuit depth reduction in feedback-based quantum optimization with a quadratic approximation |
| title_sort | scalable circuit depth reduction in feedback based quantum optimization with a quadratic approximation |
| url | http://doi.org/10.1103/PhysRevResearch.7.013035 |
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