Quantum algorithms for unsupervised machine learning and neural networks ; Algorithmes quantiques pour réseaux de neurones et apprentissage automatique non supervisé
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| Title: | Quantum algorithms for unsupervised machine learning and neural networks ; Algorithmes quantiques pour réseaux de neurones et apprentissage automatique non supervisé |
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| Authors: | Landman, Jonas |
| Contributors: | Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Université Paris Cité, Iordanis Kerenidis |
| Source: | https://theses.hal.science/tel-03850789 ; Computer science. Université Paris Cité, 2021. English. ⟨NNT : 2021UNIP7140⟩. |
| Publisher Information: | CCSD |
| Publication Year: | 2021 |
| Subject Terms: | Quantum Computing, Quantum Computer, Quantum Algorithms, Artificial Intelligence, Machine Learning, Neural Networks, Deep Learning, Unsupervised Learning, Clustering, Ordinateur Quantique, Algorithmes Quantiques, [SCCO.COMP]Cognitive science/Computer science |
| Description: | In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning. 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 will 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 equivalents to their classical version, regarding the computational complexity, but exhibit random effects due to the quantum nature of the computation. Many simulations have been carried out to study these effects and measure the learning accuracy of our quantum algorithms on real data. Finally, we will present a quantum orthogonal neural network circuit adapted to the currently available small and imperfect quantum computers (NISQ). This allows us to perform experiments on real quantum computers to test our theory. ; Cette thèse vise à étudier si les algorithmes quantiques peuvent être utilisés dans le domaine de l'apprentissage automatique, ou intelligence artificielle. Nous rappelons d'abord les principes fondamentaux de l'apprentissage automatique et de l'informatique quantique, puis nous décrivons plus précisément comment les relier par l'algèbre linéaire: nous introduisons des algorithmes quantiques pour résoudre efficacement des tâches telles que le produit de matrices ou l'estimation de distances. Ces résultats sont ensuite utilisés pour développer de nouveaux algorithmes quantiques pour l'apprentissage automatique non ... |
| Document Type: | doctoral or postdoctoral thesis |
| Language: | English |
| Relation: | NNT: 2021UNIP7140 |
| Availability: | https://theses.hal.science/tel-03850789 https://theses.hal.science/tel-03850789v1/document https://theses.hal.science/tel-03850789v1/file/va_Landman_Jonas.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| Accession Number: | edsbas.B0B5A4E3 |
| Database: | BASE |
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