Dr Ilaria Siloi

Tensor Network applications to optimization problems

Tensor network (TN) methods have been successfully applied in various fields, including quantum many-body systems and machine learning. In this talk, we explore TN applications for optimization problems. Firstly, we address mission planning for satellites in earth observation, optimizing satellite schedules based on user requests within a given timeframe. The original knapsack formulation including several constraints, is mapped into a QUBO formulation. We demonstrate the efficacy of TN methods in finding ground-state solutions that meet these constraints. Additionally, we tackle lattice-based cryptography for RSA prime factorization. We develop a TN approach to improve Schnorr's algorithm, encoding prime factors into optimal solutions of NP-hard instances of the closest vector problem (CVP). Our TN method efficiently extracts optimal solutions from these CVPs spectra and successfully factorizes RSA semiprimes up to over 100 bits, marking the largest RSA number factored using Schnorr’s sieving method to date.