Computational approaches to Quantum complexity and the many-body problem

The main purpose of the research project is to understand complexity in the context of the many-body problem, with particular reference to quantum simulators.Computational methods drawn from statistical mechanics, such as Monte Carlo methods and tensor networks, will be developed and employed. These methods will be used to quantify various measures of complexity: measures of quantum computational complexity such as entanglement and non-stabilizerness, and measures of algorithmic complexity based on non-parametric learning methods. The models of interest will include both paradigmatic examples of quantum statistical mechanics and models inspired by experiments with synthetic systems.