Recursive QAOA outperforms the original QAOA for the MAX-CUT problem on complete graphs

Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve combinatorial optimization problems such as the MAX-CUT problem. In spite of its potential for near-term quantum applications, it has been known that quantum approximate op...

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Veröffentlicht in:Quantum information processing Jg. 23; H. 3
Hauptverfasser: Bae, Eunok, Lee, Soojoon
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 26.02.2024
Schlagworte:
Data Structures and Information Theory
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
Complete graphs
68Q12
81P68
Recursive quantum approximate optimization algorithms
MAX-CUT problem
ISSN:1573-1332, 1573-1332
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Abstract Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve combinatorial optimization problems such as the MAX-CUT problem. In spite of its potential for near-term quantum applications, it has been known that quantum approximate optimization algorithms have limitations for certain instances to solve the MAX-CUT problem, at any constant level p . Recently, the recursive quantum approximate optimization algorithm, which is a non-local version of quantum approximate optimization algorithm, has been proposed to overcome these limitations. However, it has been shown by mostly numerical evidences that the recursive quantum approximate optimization algorithm outperforms the original quantum approximate optimization algorithm for specific instances. In this paper, we analytically prove that the recursive quantum approximate optimization algorithm is more competitive than the original one to solve the MAX-CUT problem for complete graphs with respect to the approximation ratio.
AbstractList Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve combinatorial optimization problems such as the MAX-CUT problem. In spite of its potential for near-term quantum applications, it has been known that quantum approximate optimization algorithms have limitations for certain instances to solve the MAX-CUT problem, at any constant level p . Recently, the recursive quantum approximate optimization algorithm, which is a non-local version of quantum approximate optimization algorithm, has been proposed to overcome these limitations. However, it has been shown by mostly numerical evidences that the recursive quantum approximate optimization algorithm outperforms the original quantum approximate optimization algorithm for specific instances. In this paper, we analytically prove that the recursive quantum approximate optimization algorithm is more competitive than the original one to solve the MAX-CUT problem for complete graphs with respect to the approximation ratio.
ArticleNumber 78
Author Lee, Soojoon
Bae, Eunok
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  email: level@khu.ac.kr
  organization: Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University
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Cites_doi 10.1103/PhysRevA.97.022304
10.22331/q-2021-04-20-437
10.22331/q-2022-03-30-678
10.1103/PhysRevLett.125.260505
10.22331/q-2018-08-06-79
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Keywords Complete graphs
68Q12
81P68
Recursive quantum approximate optimization algorithms
MAX-CUT problem
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Snippet Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve combinatorial optimization...
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SubjectTerms Data Structures and Information Theory
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
Title Recursive QAOA outperforms the original QAOA for the MAX-CUT problem on complete graphs
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