Quantum Entanglement and Machine Learning

Quantum entanglement has been studied extensively by the quantum information community, mostly in the context of discrete systems (such as chains and lattices of spins). Over the last decade, there has been considerable progress in defining quantum entanglement in the context of quantum field theories. Deep relationships have been uncovered between quantum entanglement and the underlying geometry encapsulating renormalisation group flow (renormalisation group flow describes the transition from physics at small scales to physics at large scales). In turn, this underlying geometry of the renormalisation group flow can be interpreted in terms of a machine learning process. The main goal of this project is to develop precise quantitative relationships between the geometries of renormalisation group flows and (quantum) machine learning processes. Given such relations, we will then explore whether quantum algorithms can be used to develop and improve existing (classical) algorithms for machine learning.

This project will build on foundations of quantum physics/quantum field theory. It requires putting together ideas from mathematics, physics and theoretical computer science. The exploration of renormalisation group geometries will use concepts from topology and differential geometry while the machine learning aspect of the project requires understanding of algorithms and networks.