Abstract
We introduce a novel approach to translate arbitrary 3-sat instances to Quadratic Unconstrained Binary Optimization (qubo) as they are used by quantum annealing (QA) or the quantum approximate optimization algorithm (QAOA). Our approach requires fewer couplings and fewer physical qubits than the current state-of-the-art, which results in higher solution quality. We verified the practical applicability of the approach by testing it on a D-Wave quantum annealer.
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References
Arute, F., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505–510 (2019)
Bian, Z., Chudak, F., Macready, W., Roy, A., Sebastiani, R., Varotti, S.: Solving SAT and MaxSAT with a quantum annealer: foundations and a preliminary report. In: Dixon, C., Finger, M. (eds.) FroCoS 2017. LNCS (LNAI), vol. 10483, pp. 153–171. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66167-4_9
Boothby, K., Bunyk, P., Raymond, J., Roy, A.: Next-generation topology of D-Wave quantum processors. arXiv preprint arXiv:2003.00133 (2020)
Cai, J., Macready, W.G., Roy, A.: A practical heuristic for finding graph minors. arXiv preprint arXiv:1406.2741 (2014)
Chancellor, N., Zohren, S., Warburton, P.A., Benjamin, S.C., Roberts, S.: A direct mapping of max k-sat and high order parity checks to a chimera graph. Sci. Rep. 6(1), 1–9 (2016)
Choi, V.: Adiabatic quantum algorithms for the NP-complete maximum-weight independent set, exact cover and 3SAT problems. arXiv preprint arXiv:1004.2226 (2010)
Cook, S.: The P versus NP problem. In: The Millennium Prize Problems, pp. 87–104 (2006)
Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the 3rd Annual ACM Symposium on Theory of Computing. ACM (1971)
Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028 (2014)
Feld, S., et al.: A hybrid solution method for the capacitated vehicle routing problem using a quantum annealer. arXiv preprint arXiv:1811.07403 (2018)
Fortnow, L.: The status of the P versus NP problem. Commun. ACM 52(9), 78–86 (2009)
Gabor, T., et al.: Assessing solution quality of 3SAT on a quantum annealing platform. In: Feld, S., Linnhoff-Popien, C. (eds.) QTOP 2019. LNCS, vol. 11413, pp. 23–35. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-14082-3_3
Glover, F., Kochenberger, G., Du, Y.: A tutorial on formulating and using QUBO models. arXiv preprint arXiv:1811.11538 (2018)
Hen, I., Spedalieri, F.M.: Quantum annealing for constrained optimization. Phys. Rev. Appl. 5(3), 034007 (2016)
Hogg, T.: Adiabatic quantum computing for random satisfiability problems. Phys. Rev. A 67(2), 022314 (2003)
Johnson, M.W., et al.: Quantum annealing with manufactured spins. Nature 473(7346), 194–198 (2011)
Kadowaki, T., Nishimori, H.: Quantum annealing in the transverse Ising model. Phys. Rev. E 58(5), 5355 (1998)
Lucas, A.: Ising formulations of many np problems. Front. Phys. 2, 5 (2014)
McGeoch, C.C., Wang, C.: Experimental evaluation of an adiabiatic quantum system for combinatorial optimization. In: Proceedings of the ACM International Conference on Computing Frontiers, pp. 1–11 (2013)
Mooney, G.J., Tonetto, S.U., Hill, C.D., Hollenberg, L.C.: Mapping NP-hard problems to restricted adiabatic quantum architectures. arXiv preprint arXiv:1911.00249 (2019)
Nüßlein, J., Gabor, T., Linnhoff-Popien, C., Feld, S.: Algorithmic QUBO formulations for K-SAT and Hamiltonian cycles. arXiv preprint arXiv:2204.13539 (2022)
Nüßlein, J., Roch, C., Gabor, T., Linnhoff-Popien, C., Feld, S.: Black box optimization using QUBO and the cross entropy method. arXiv preprint arXiv:2206.12510 (2022)
Venturelli, D., Marchand, D.J., Rojo, G.: Quantum annealing implementation of job-shop scheduling. arXiv preprint arXiv:1506.08479 (2015)
Zahedinejad, E., Zaribafiyan, A.: Combinatorial optimization on gate model quantum computers: a survey. arXiv preprint arXiv:1708.05294 (2017)
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Nüßlein, J., Zielinski, S., Gabor, T., Linnhoff-Popien, C., Feld, S. (2023). Solving (Max) 3-SAT via Quadratic Unconstrained Binary Optimization. In: Mikyška, J., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M. (eds) Computational Science – ICCS 2023. ICCS 2023. Lecture Notes in Computer Science, vol 14077. Springer, Cham. https://doi.org/10.1007/978-3-031-36030-5_3
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