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

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.

8 pages, 1 figure

References in corpus (1)

• Local classical MAX-CUT algorithm outperforms $p=2$ QAOA on high-girth regular graphs

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• A Review on Quantum Approximate Optimization Algorithm and its Variants
• Approximating under the Influence of Quantum Noise and Compute Power
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• Missing Puzzle Pieces in the Performance Landscape of the Quantum Approximate Optimization Algorithm
• Predict and Conquer: Navigating Algorithm Trade-offs with Quantum Design Automation
• Q-CHOP: Quantum constrained Hamiltonian optimization