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 a simple 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. In a recent patent, we proposed to increase the efficiency of QAOA by adding symmetry-breaking (unitary or symplectic) terms to the quantum problem. The student shall explore the impact of these terms in other models, the probability distribution of the cost, and, in particular, the effect of a dissipative environment and dephasing. Realizations on existing quantum architectures shall also be considered. This research plan may be also considered as a KDP project.