Simone Warzel

Adiabatic quantum computing was proposed to speed up the search of minima in a complex energy landscape. Its limitations are well known and have been quantified in terms of lower bounds on its  run time. In this talk, after a brief review, I will explain how to turn these lower bounds into estimates on the spectral gap of the involved generators of the quantum evolution. I will illustrate these ideas by applying them for a proof of the ground state phase transition in the quantum random energy model (QREM), i.e., Derrida’s famous mean-field spin glass with a transversal constant magnetic field.