QAOA (Quantum Approximate Optimization Approach) and AQA (Adiabatic Quantum Algorithm) are quantum optimization methods, where the classical ground state of a system is reached by deforming the quantum state. These quantum deformations result in quantum models such as the quantum XORSAT problem or the quantum traveling agent problem, some of which appear to possess a glassy phase. The goal of the student shall be to study the structure of the phase diagram of these models as well as their properties from the point of view of many-body localization. For this purpose, the student will combine the so-called quantum cavity approach with exact diagonalization and variational methods. Realization on existing quantum architectures shall also be considered.