A Resource-Efficient Quantum Framework for Graph Coloring and Chromatic Number Estimation

Francesco Turro; Daniele Dragoni

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arXiv · 2608.08694

A Resource-Efficient Quantum Framework for Graph Coloring and Chromatic Number Estimation

Francesco Turro·Daniele Dragoni

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Abstract

Many industrial optimization tasks can be modeled as graph coloring, where adjacent vertices must have different colors. This NP-hard problem is challenging for large graphs. We present a quantum encoding requiring qubits that scale logarithmically with the number of colors and linearly with vertices. Using adiabatic evolution with a novel mixer Hamiltonian and vertex terms, we compute the chromatic number and demonstrate robustness by solving constrained truck loading problems.

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Francesco Turro, Daniele Dragoni. 2026-08-09. A Resource-Efficient Quantum Framework for Graph Coloring and Chromatic Number Estimation. https://arxiv.org/abs/2608.08694

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