  In this thesis, we investigate whether quantum algorithms can be used in the
field of machine learning for both long and near term quantum computers. We
will first recall the fundamentals of machine learning and quantum computing
and then describe more precisely how to link them through linear algebra: we
introduce quantum algorithms to efficiently solve tasks such as matrix product
or distance estimation. These results are then used to develop new quantum
algorithms for unsupervised machine learning, such as k-means and spectral
clustering. This allows us to define many fundamental procedures, in particular
in vector and graph analysis. We will also present new quantum algorithms for
neural networks, or deep learning. For this, we introduce an algorithm to
perform a quantum convolution product on images, as well as a new way to
perform a fast tomography on quantum states. We prove that these quantum
algorithms are faster versions of equivalent classical algorithms, but exhibit
random effects due to the quantum nature of the computation. Many simulations
have been carried out to study these effects and measure their learning
accuracy on real data. Finally, we will present a quantum orthogonal neural
network circuit adapted to the currently available small and imperfect quantum
computers. This allows us to perform real experiments to test our theory.
