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 algorithms performance by considering complete and ErdH{o}s-Renyi 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 algorithms performance.
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