Solving correlation clustering with QAOA and a Rydberg qudit system: a full-stack approach

• URL: http://arxiv.org/abs/2106.11672v3
• Date: Fri, 25 Mar 2022 14:06:29 GMT
• Title: Solving correlation clustering with QAOA and a Rydberg qudit system: a full-stack approach
• Authors: Jordi R. Weggemans, Alexander Urech, Alexander Rausch, Robert Spreeuw, Richard Boucherie, Florian Schreck, Kareljan Schoutens, Ji\v{r}\'i Min\'a\v{r} and Florian Speelman
• Abstract summary: We study the correlation clustering problem using the quantum approximate optimization algorithm (QAOA) and qudits. Specifically, we consider a neutral atom quantum computer and propose a full stack approach for correlation clustering. We show the qudit implementation is superior to the qubit encoding as quantified by the gate count.
• Score: 94.37521840642141
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the correlation clustering problem using the quantum approximate optimization algorithm (QAOA) and qudits, which constitute a natural platform for such non-binary problems. Specifically, we consider a neutral atom quantum computer and propose a full stack approach for correlation clustering, including Hamiltonian formulation of the algorithm, analysis of its performance, identification of a suitable level structure for ${}^{87}{\rm Sr}$ and specific gate design. We show the qudit implementation is superior to the qubit encoding as quantified by the gate count. For single layer QAOA, we also prove (conjecture) a lower bound of $0.6367$ ($0.6699$) for the approximation ratio on 3-regular graphs. Our numerical studies evaluate the algorithm's performance by considering complete and Erd\H{o}s-R\'enyi graphs of up to 7 vertices and clusters. We find that in all cases the QAOA surpasses the Swamy bound $0.7666$ for the approximation ratio for QAOA depths $p \geq 2$. Finally, by analysing the effect of errors when solving complete graphs we find that their inclusion severely limits the algorithm's performance.

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