Large-Scale Quantum Approximate Optimization via Divide-and-Conquer

Quantum approximate optimization algorithm (QAOA) is a promising hybrid quantum-classical algorithm for solving combinatorial optimization problems. However, it cannot overcome qubit limitation for large-scale problems. Furthermore, the simulation time of QAOA scales poorly with the problem size. We...

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Veröffentlicht in:	IEEE transactions on computer-aided design of integrated circuits and systems Jg. 42; H. 6; S. 1852 - 1860
Hauptverfasser:	Li, Junde, Alam, Mahabubul, Ghosh, Swaroop
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.06.2023 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Approximation algorithms Chemical partition Combinatorial analysis Computers Graph maxcut Graph theory Logic gates noisy intermediate-scale quantum computing (QC) Optimization Partitioning Partitioning algorithms Polynomials quantum approximate optimization algorithm (QAOA) Quantum computers Quantum computing Qubit Qubits (quantum computing) Reconstruction
ISSN:	0278-0070, 1937-4151
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Abstract	Quantum approximate optimization algorithm (QAOA) is a promising hybrid quantum-classical algorithm for solving combinatorial optimization problems. However, it cannot overcome qubit limitation for large-scale problems. Furthermore, the simulation time of QAOA scales poorly with the problem size. We propose a divide-and-conquer QAOA (DC-QAOA) to address the above challenges for graph maximum cut (MaxCut) problem. The algorithm works by recursively partitioning a larger graph into smaller ones whose MaxCut solutions are obtained with small-size noisy intermediate-scale quantum computers. The overall solution is retrieved from the subsolutions by applying the combination policy of measurement distribution reconstruction (MDR). The solution quality depends on the graph partitioning algorithm and MDR policy. Multiple partitioning and reconstruction methods are proposed and compared. Results are evaluated by metrics, such as quantum program runtime, measurement expectation value (EV), and approximation ratio (AR). The results show that DC-QAOA achieves 97.14% AR (20.32% higher than classical counterpart), and 94.79% EV (15.80% higher than quantum annealing). DC-QAOA solves large-scale graph instances with a polynomial rate or returns unsuccessful partition if graph connectivity requirement is not fulfilled otherwise.
AbstractList	Quantum approximate optimization algorithm (QAOA) is a promising hybrid quantum-classical algorithm for solving combinatorial optimization problems. However, it cannot overcome qubit limitation for large-scale problems. Furthermore, the simulation time of QAOA scales poorly with the problem size. We propose a divide-and-conquer QAOA (DC-QAOA) to address the above challenges for graph maximum cut (MaxCut) problem. The algorithm works by recursively partitioning a larger graph into smaller ones whose MaxCut solutions are obtained with small-size noisy intermediate-scale quantum computers. The overall solution is retrieved from the subsolutions by applying the combination policy of measurement distribution reconstruction (MDR). The solution quality depends on the graph partitioning algorithm and MDR policy. Multiple partitioning and reconstruction methods are proposed and compared. Results are evaluated by metrics, such as quantum program runtime, measurement expectation value (EV), and approximation ratio (AR). The results show that DC-QAOA achieves 97.14% AR (20.32% higher than classical counterpart), and 94.79% EV (15.80% higher than quantum annealing). DC-QAOA solves large-scale graph instances with a polynomial rate or returns unsuccessful partition if graph connectivity requirement is not fulfilled otherwise.
Author	Li, Junde Ghosh, Swaroop Alam, Mahabubul
Author_xml	– sequence: 1 givenname: Junde orcidid: 0000-0003-2470-8233 surname: Li fullname: Li, Junde email: jul1512@psu.edu organization: Department of Computer Science and Engineering, The Pennsylvania State University, State College, PA, USA – sequence: 2 givenname: Mahabubul orcidid: 0000-0003-1441-2623 surname: Alam fullname: Alam, Mahabubul organization: Department of Electrical Engineering, The Pennsylvania State University, State College, PA, USA – sequence: 3 givenname: Swaroop orcidid: 0000-0001-8753-490X surname: Ghosh fullname: Ghosh, Swaroop organization: School of Electrical Engineering and Computer Science, The Pennsylvania State University, State College, PA, USA
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SubjectTerms	Algorithms Approximation algorithms Chemical partition Combinatorial analysis Computers Graph maxcut Graph theory Logic gates noisy intermediate-scale quantum computing (QC) Optimization Partitioning Partitioning algorithms Polynomials quantum approximate optimization algorithm (QAOA) Quantum computers Quantum computing Qubit Qubits (quantum computing) Reconstruction
Title	Large-Scale Quantum Approximate Optimization via Divide-and-Conquer
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