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

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 Sr-87 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 ErdOs-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 >= 2. Finally, by analysing the effect of errors when solving complete graphs we find that their inclusion severely limits the algorithm's performance.