Nicolò Vescera

Fabrizio Fagiolo, Nicolò Vescera

In this paper we present a variational algorithm for the Traveling Salesman Problem (TSP) that combines (i) a compact encoding of permutations, which reduces the qubit requirement too, (ii) an optimize-freeze-reuse strategy: where the circuit topology (``Ansatz'') is first optimized on a training instance by Simulated Annealing (SA), then ``frozen'' and re-used on novel instances, limited to a rapid re-optimization of only the circuit parameters. This pipeline eliminates costly structural research in testing, making the procedure immediately implementable on NISQ hardware. On a set of $40$ randomly generated symmetric instances that span $4 - 7$ cities, the resulting Ansatz achieves an average optimal trip sampling probability of $100\%$ for 4 city cases, $90\%$ for 5 city cases and $80\%$ for 6 city cases. With 7 cities the success rate drops markedly to an average of $\sim 20\%$, revealing the onset of scalability limitations of the proposed method. The results show robust generalization ability for moderate problem sizes and indicate how freezing the Ansatz can dramatically reduce time-to-solution without degrading solution quality. The paper also discusses scalability limitations, the impact of ``warm-start'' initialization of parameters, and prospects for extension to more complex problems, such as Vehicle Routing and Job-Shop Scheduling.

Lucrezia Rinelli, Arianna Travaglini, Nicolò Vescera et al.

This study evaluates two approaches applied to computed tomography (CT) images of patients with abdominal aortic aneurysm: one deterministic, based on tools of Approximation Theory, and one based on Artificial Intelligence. Both aim to segment the basal CT images to extract the patent area of the aortic vessel, in order to propose an alternative to nephrotoxic contrast agents for diagnosing this pathology. While the deterministic approach employs sampling Kantorovich operators and the theory behind, leveraging the reconstruction and enhancement capabilities of these operators applied to images, the artificial intelligence-based approach lays on a U-net neural network. The results obtained from testing the two methods have been compared numerically and visually to assess their performances, demonstrating that both models yield accurate results.