Tensor Network Approaches to Combinatorial Optimization Problems in Satellite Mission Planning for Earth Observation

Combinatorial optimization problems are central to many real-world applications but are often computationally intractable due to their NP-hard nature. While quantum computing holds promise for solving certain problems efficiently, current hardware limitations in the NISQ era hinder its scalability. This thesis explores a quantum-inspired approach using Tensor Networks (TNs) to address a real-world mission planning (MP) problem for Earth observation involving a cluster of satellites, modeled as a multivariable knapsack problem. In this thesis, we introduce a novel qudit-based mapping that encodes multiple binary decision variables into single qudits, allowing for a more compact and constraint-aware formulation. This mapping translates the optimization problem into the task of finding the ground state of a many-qudit Hamiltonian. Initial validation is performed via exact diagonalization on small instances. To extend the approach to real-world instances, we approach the ground state search using TN methods. Finally, the performance and scalability of the proposed qudit mapping are evaluated against standard qubit-based formulations and state-of-the-art classical solvers.