Exploring the energy landscape of (quantum) optimisation problems

We give a non-technical overview of works by different groups which aim to understand the complexity of the energy landscape of optimisation problems in machine learning from the point of view of spin-glasses and random matrix theory. Interestingly, some success of deep neural networks can be explained by a change in the complexity of the energy landscape where local minima appear in a narrow energy band close to the global minimum. Finally, we mention some of our work in progress in which we perform a similar analysis for quantum optimisation problems on the D-wave system.