Quantum computing is at the cutting edge of technological innovation, offering the potential to solve complex problems that classical "binary" computers cannot address. Tensor algebra, with its comprehensive mathematical framework, offers crucial tools for modeling and approximating large multidimensional datasets. This thesis seeks to investigate the interplay between tensor networks and quantum computing by proposing original, robust (to decoherence of qubits) quantum algorithms that utilize tensor structures to improve computational efficiency and capabilities. This research requires a multidisciplinary understanding of quantum physics and linear algebra. This thesis topic will benefit from the complementary expertises of Remy
Boyer (CRISTAL/SIGMA) for the multilinear algebra aspect and Giuseppe Patera (PhLAM, Quantum Information team) for the quantum physics aspect.