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

Junde Li, Mahabubul Alam, Swaroop Ghosh

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1852-1860
Number of pages9
JournalIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Issue number6
StatePublished - Jun 1 2023

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering


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