Quantum computing is believed to offer a future advantage in a variety of algorithms, including those challenging for traditional computers (e.g., Prime Factorization). However, in an era where Noisy Quantum Computers (QCs) are the norm, practical applications of QC would be centered around optimization approaches and energy efficiency rather than purely algorithmic performance.

In this context, this PhD thesis aims to address the utilization of QC to enhance the learning process of Neural Networks (NN). The learning phase of NN is arguably the most power-hungry aspect with traditional approaches. Leveraging quantum optimization techniques or quantum linear system solving could potentially yield an energy advantage, coupled with the ability to perform the learning phase with a less extensive set of training examples.