Localization in the Constrained Quantum Annealing of Graph Coloring

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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 for the CQA of graph coloring and a set of disordered spin chains. In the model for the CQA of graph coloring, disorder corresponds to the fluctuation of effective local fields that increase in a CQA process. Numerical simulations of effective fields and entanglement demonstrate how localization appears in the CQA. Some notable features appear in the concurrence, which is a measure of entanglement, plotted as a function of the fluctuation of effective fields.

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