Algorithmic QUBO formulations for k -SAT and hamiltonian cycles

Nüßlein, Jonas; Gabor, Thomas; Linnhoff-Popien, Claudia und Feld, Sebastian (2022): Algorithmic QUBO formulations for k -SAT and hamiltonian cycles. GECCO '22: Genetic and Evolutionary Computation Conference, Boston, Massachusetts, July 9 - 13, 2022. Fieldsend, Jonathan E. (Hrsg.): In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, New York: Association for Computing Machinery. S. 2240-2246

Abstract

Quadratic Unconstrained Binary Optimization (QUBO) can be seen as a generic language for optimization problems. QUBOs attract particular attention since they can be solved with quantum hardware, like quantum annealers or quantum gate computers running QAOA. In this paper, we present two novel QUBO formulations for k-SAT and Hamiltonian Cycles that scale significantly better than existing approaches. For k-SAT we reduce the growth of the QUBO matrix from O(k) to O(log(k)). For Hamiltonian Cycles the matrix no longer grows quadratically in the number of nodes, as currently, but linearly in the number of edges and logarithmically in the number of nodes.

We present these two formulations not as mathematical expressions, as most QUBO formulations are, but as meta-algorithms that facilitate the design of more complex QUBO formulations and allow easy reuse in larger and more complex QUBO formulations.

• Dokumententyp: Konferenzbeitrag (Paper)
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• Ort: New York
• Bemerkung: ISBN 978-1-4503-9268-6
• Sprache: Englisch