Modified recursive QAOA for exact MAX-CUT solutions on bipartite graphs: closing the gap beyond QAOA limit

Quantum approximate optimization algorithm (QAOA) is a quantum–classical hybrid algorithm proposed with the goal of approximately solving combinatorial optimization problems such as the MAX-CUT problem. It has been considered a potential candidate for achieving quantum advantage in the noisy interme...

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Vydáno v:	Journal of physics. A, Mathematical and theoretical Ročník 58; číslo 48
Hlavní autoři:	Bae, Eunok, Kwon, Hyukjoon, Vijendran, V, Lee, Soojoon
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	IOP Publishing 28.11.2025
Témata:	bipartite graphs MAX-CUT problem quantum approximate optimization algorithm recursive quantum approximate optimization algorithm
ISSN:	1751-8113, 1751-8121
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Popis
Shrnutí:	Quantum approximate optimization algorithm (QAOA) is a quantum–classical hybrid algorithm proposed with the goal of approximately solving combinatorial optimization problems such as the MAX-CUT problem. It has been considered a potential candidate for achieving quantum advantage in the noisy intermediate-scale quantum era and has been extensively studied. However, the performance limitations of low-level QAOA have also been demonstrated across various instances. In this work, we first analytically prove the performance limitations of the standard level-1 QAOA in solving the MAX-CUT problem on bipartite graphs. To this end, we derive an upper bound for the approximation ratio based on the average degree of bipartite graphs. Second, we demonstrate that recursive QAOA (RQAOA), which recursively reduces graph size using QAOA as a subroutine, outperforms the standard level-1 QAOA. However, the performance of RQAOA exhibits limitations as the graph size increases. Finally, we show that RQAOA with a restricted parameter regime can fully address these limitations. Surprisingly, this modified RQAOA always finds the exact maximum cut for any bipartite graphs and even for a more general graph with parity-signed weights.
Bibliografie:	JPhysA-122842.R2
ISSN:	1751-8113 1751-8121
DOI:	10.1088/1751-8121/ae20d7