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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Bibliographic Details
Published in:IEEE transactions on computer-aided design of integrated circuits and systems Vol. 42; no. 6; pp. 1852 - 1860
Main Authors: Li, Junde, Alam, Mahabubul, Ghosh, Swaroop
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0278-0070
1937-4151
DOI:10.1109/TCAD.2022.3212196