# Localization in the constrained quantum annealing of graph coloring

## TL;DR

This paper investigates how localization phenomena emerge in constrained quantum annealing for graph coloring, revealing the role of disorder and entanglement in the process through numerical simulations.

## Contribution

It introduces a model linking constrained quantum annealing of graph coloring to disordered spin chains and analyzes localization effects via numerical simulations.

## Key findings

- Localization appears in the CQA process.
- Entanglement measures show notable features related to disorder.
- Disorder fluctuations influence effective local fields.

## Abstract

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.