Mean-Field Approximate Optimization Algorithm
The quantum approximate optimization algorithm (QAOA) is suggested as a promising application on early quantum computers. Here a quantum-inspired classical algorithm, the mean-field approximate optimization algorithm (mean-field AOA), is developed by replacement of the quantum evolution of the QAOA...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-09-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.4.030335 |
| _version_ | 1827820408640897024 |
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| author | Aditi Misra-Spieldenner Tim Bode Peter K. Schuhmacher Tobias Stollenwerk Dmitry Bagrets Frank K. Wilhelm |
| author_facet | Aditi Misra-Spieldenner Tim Bode Peter K. Schuhmacher Tobias Stollenwerk Dmitry Bagrets Frank K. Wilhelm |
| author_sort | Aditi Misra-Spieldenner |
| collection | DOAJ |
| description | The quantum approximate optimization algorithm (QAOA) is suggested as a promising application on early quantum computers. Here a quantum-inspired classical algorithm, the mean-field approximate optimization algorithm (mean-field AOA), is developed by replacement of the quantum evolution of the QAOA with classical spin dynamics through the mean-field approximation. Because of the alternating structure of the QAOA, this classical dynamics can be found exactly for any number of QAOA layers. We benchmark its performance against the QAOA on the Sherrington-Kirkpatrick model and the partition problem, and find that the mean-field AOA outperforms the QAOA in both cases for most instances. Our algorithm can thus serve as a tool to delineate optimization problems that can be solved classically from those that cannot, i.e., we believe that it will help to identify instances where a true quantum advantage can be expected from the QAOA. To quantify quantum fluctuations around the mean-field trajectories, we solve an effective scattering problem in time, which is characterized by a spectrum of time-dependent Lyapunov exponents. These provide an indicator for the hardness of a given optimization problem relative to the mean-field AOA. |
| first_indexed | 2024-03-12T01:27:23Z |
| format | Article |
| id | doaj.art-898328ec939c4a499fc6b32839b3435d |
| institution | Directory Open Access Journal |
| issn | 2691-3399 |
| language | English |
| last_indexed | 2024-03-12T01:27:23Z |
| publishDate | 2023-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj.art-898328ec939c4a499fc6b32839b3435d2023-09-12T14:23:04ZengAmerican Physical SocietyPRX Quantum2691-33992023-09-014303033510.1103/PRXQuantum.4.030335Mean-Field Approximate Optimization AlgorithmAditi Misra-SpieldennerTim BodePeter K. SchuhmacherTobias StollenwerkDmitry BagretsFrank K. WilhelmThe quantum approximate optimization algorithm (QAOA) is suggested as a promising application on early quantum computers. Here a quantum-inspired classical algorithm, the mean-field approximate optimization algorithm (mean-field AOA), is developed by replacement of the quantum evolution of the QAOA with classical spin dynamics through the mean-field approximation. Because of the alternating structure of the QAOA, this classical dynamics can be found exactly for any number of QAOA layers. We benchmark its performance against the QAOA on the Sherrington-Kirkpatrick model and the partition problem, and find that the mean-field AOA outperforms the QAOA in both cases for most instances. Our algorithm can thus serve as a tool to delineate optimization problems that can be solved classically from those that cannot, i.e., we believe that it will help to identify instances where a true quantum advantage can be expected from the QAOA. To quantify quantum fluctuations around the mean-field trajectories, we solve an effective scattering problem in time, which is characterized by a spectrum of time-dependent Lyapunov exponents. These provide an indicator for the hardness of a given optimization problem relative to the mean-field AOA.http://doi.org/10.1103/PRXQuantum.4.030335 |
| spellingShingle | Aditi Misra-Spieldenner Tim Bode Peter K. Schuhmacher Tobias Stollenwerk Dmitry Bagrets Frank K. Wilhelm Mean-Field Approximate Optimization Algorithm PRX Quantum |
| title | Mean-Field Approximate Optimization Algorithm |
| title_full | Mean-Field Approximate Optimization Algorithm |
| title_fullStr | Mean-Field Approximate Optimization Algorithm |
| title_full_unstemmed | Mean-Field Approximate Optimization Algorithm |
| title_short | Mean-Field Approximate Optimization Algorithm |
| title_sort | mean field approximate optimization algorithm |
| url | http://doi.org/10.1103/PRXQuantum.4.030335 |
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