Quantum algorithms achieve O(1.9140^n) time for chromatic number with QRAM and O(1.9575^n) for 20-coloring in polynomial space by combining quantum dynamic programming with Grover search on branching algorithms.
Fomin, Serge Gaspers, and Saket Saurabh
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Exponential-time quantum algorithms for graph coloring problems
Quantum algorithms achieve O(1.9140^n) time for chromatic number with QRAM and O(1.9575^n) for 20-coloring in polynomial space by combining quantum dynamic programming with Grover search on branching algorithms.