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 87Sr 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 Erdős-Rényi 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

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 87Sr 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 Erdős-Rényi 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

Topological properties of a dense atomic lattice gas

We investigate the existence of topological phases in a dense two-dimensional atomic lattice gas. The coupling of the atoms to the radiation field gives rise to dissipation and a nontrivial coherent long-range exchange interaction whose form goes beyond a simple power law. The far-field terms of the potential—which are particularly relevant for atomic separations comparable to the atomic transition wavelength—can give rise to energy spectra with one-sided divergences in the Brillouin zone. The long-ranged character of the interactions has another important consequence: it can break the standard bulk-boundary relation in topological insulators. We show that topological properties such as the transport of an excitation along the edge of the lattice are robust with respect to the presence of lattice defects and dissipation. The latter is of particular relevance as dissipation and coherent interactions are inevitably connected in our setting