Hybrid quantum-classical algorithms for approximate graph coloring

We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX- k -CUT, the problem of finding an approximate k -vertex coloring of a graph. We compare this proposal to the best known classical and hybrid classical-quantum algorithms. First, we show that the standard (n...

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Bibliographic Details
Published in:	Quantum (Vienna, Austria) Vol. 6; p. 678
Main Authors:	Bravyi, Sergey, Kliesch, Alexander, Koenig, Robert, Tang, Eugene
Format:	Journal Article
Language:	English
Published:	Austria Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften 30.03.2022 Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
ISSN:	2521-327X, 2521-327X
Online Access:	Get full text
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Summary:	We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX- k -CUT, the problem of finding an approximate k -vertex coloring of a graph. We compare this proposal to the best known classical and hybrid classical-quantum algorithms. First, we show that the standard (non-recursive) QAOA fails to solve this optimization problem for most regular bipartite graphs at any constant level p : the approximation ratio achieved by QAOA is hardly better than assigning colors to vertices at random. Second, we construct an efficient classical simulation algorithm which simulates level- 1 QAOA and level- 1 RQAOA for arbitrary graphs. In particular, these hybrid algorithms give rise to efficient classical algorithms, and no benefit arising from the use of quantum mechanics is to be expected. Nevertheless, they provide a suitable testbed for assessing the potential benefit of hybrid algorithm: We use the simulation algorithm to perform large-scale simulation of level- 1 QAOA and RQAOA with up to 300 qutrits applied to ensembles of randomly generated 3 -colorable constant-degree graphs. We find that level- 1 RQAOA is surprisingly competitive: for the ensembles considered, its approximation ratios are often higher than those achieved by the best known generic classical algorithm based on rounding an SDP relaxation. This suggests the intriguing possibility that higher-level RQAOA may be a potentially useful algorithm for NISQ devices.
Bibliography:	USDOE SC0018407; PHY-1733907
ISSN:	2521-327X 2521-327X
DOI:	10.22331/q-2022-03-30-678