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arXiv · 2307.05821

Extending relax-and-round combinatorial optimization solvers with quantum correlations

Maxime Dupont·Bhuvanesh Sundar
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Abstract

We introduce a relax-and-round approach embedding the quantum approximate optimization algorithm (QAOA) with $p\geq 1$ layers. We show for many problems, including Sherrington-Kirkpatrick spin glasses, that at $p=1$, it is as accurate as its classical counterpart, and maintains the infinite-depth optimal performance guarantee of the QAOA. Employing a different rounding scheme, we prove the method shares the performance of the Goemans-Williamson algorithm for the maximum cut problem on certain graphs. We pave the way for an overarching quantum relax-and-round framework with performance on par with some of the best classical algorithms.

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Maxime Dupont, Bhuvanesh Sundar. 2023-07-11. Extending relax-and-round combinatorial optimization solvers with quantum correlations. https://doi.org/10.1103/physreva.109.012429

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