Localization in the constrained quantum annealing of graph coloring

Constrained quantum annealing (CQA) is a quantum annealing approach that is designed so that constraints are satisfied without penalty terms. There is an analogy between the model used for the CQA of graph coloring and a disordered spin chain. In a strongly disordered spin chain, localization phenomena such as Anderson localization and many-body localization occurs. In the model for the CQA of graph coloring, disorder corresponds to the fluctuation of local effective fields that increase in a CQA process. Several measures of entanglement show how localization appears in a CQA process, depending on the fluctuation of effective fields. Localization in CQA is also considered as Anderson localization in Fock space. The CQA approach of graph coloring causes extra localization due to degenerated ground states of the problem Hamiltonian and a specific choice of the driver Hamiltonian.