PhD - "Optimization and generalization capacity of quantum machine learning algorithms" F/M

about the role

In a context of malware detection, and in a desire to improve our artificial intelligence of our artificial intelligence algorithms, the PhD student will work on several aspects of quantum machine learning, aiming at optimizing existing algorithms.
Placing himself in a context of little data and few resources available on current quantum machines, the PhD student will have to become familiar with the tools of quantum machine learning, and understand the use of Fisher information matrices. Indeed, the information matrix is obtained from the quantum circuit used, and its rank is closely related to the dimension of the ambient Hilbert space and to the expressiveness of the circuit, i.e. the capacity to explore a more or less vast region of this space. We can quote in particular the works of D. Sutter and A. Abbas ([1], [2]) who relate the Fisher information matrix to the effective dimension of a model, which allows to measure the capacity and expressiveness of the model [8]. Better mastering our ability to explore the ambient Hilbert space from a quantum model allows us to optimize the learning of the model, and thus to succeed with less data to obtain satisfactory results.

The Fisher information matrices, and more particularly their rank, are also linked to the dimension of the Lie algebra generated from the quantum gates used by the quantum model. The PhD student will thus be led to study Lie theory and group representations, which are sources of information in order to choose the quantum models to be used according to certain particularities observed on the input data. This is based on the work of M. Cerezo [3][4][6][7] who studies in particular the symmetries present in the input data in order to propose quantum algorithms respecting these symmetries, called equivariants, and thus allowing a better learning, from less data.
The PhD student will also study notions of over-parametrization, which limit the number of parameters to be used in a quantum algorithm by a quantity depending on the dimension of the ambient Hilbert space or of its associated Lie algebra [5]. This ensures that our algorithms are deep enough to provide optimal performance, without the need to to add superfluous parameters.

Currently, quantum computers are still subject to sources of error such as the noise induced by each quantum operation. It crucial, for a use as soon as possible, to address these issues in order to reduce the number of operations necessary to obtain a satisfactory learning.