Advertisement

Tabu-Driven Quantum Neighborhood Samplers

Conference paper
  • 70 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12692)

Abstract

Combinatorial optimization is an important application targeted by quantum computing. However, near-term hardware constraints make quantum algorithms unlikely to be competitive when compared to high-performing classical heuristics on large practical problems. One option to achieve advantages with near-term devices is to use them in combination with classical heuristics. In particular, we propose using quantum methods to sample from classically intractable distributions – which is the most probable approach to attain a true provable quantum separation in the near-term – which are used to solve optimization problems faster. We numerically study this enhancement by an adaptation of Tabu Search using the Quantum Approximate Optimization Algorithm (QAOA) as a neighborhood sampler. We show that QAOA provides a flexible tool for exploration-exploitation in such hybrid settings and can provide evidence that it can help in solving problems faster by saving many tabu iterations and achieving better solutions.

Keywords

Quantum computing Combinatorial optimization Tabu search 

Notes

Acknowledgements

CM, TB and VD acknowledge support from Total. This work was supported by the Dutch Research Council (NWO/OCW), as part of the Quantum Software Consortium programme (project number 024.003.037). This research is also supported by the project NEASQC funded from the European Union’s Horizon 2020 research and innovation programme (grant agreement No 951821).

References

  1. 1.
    Arute, F., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505–510 (2019).  https://doi.org/10.1038/s41586-019-1666-5CrossRefGoogle Scholar
  2. 2.
    Arute, F., et al.: Quantum approximate optimization of non-planar graph problems on a planar superconducting processor (2020)Google Scholar
  3. 3.
    Bäck, T.: Evolutionary Algorithms in Theory and Practice - Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford University Press, Oxford (1996)CrossRefGoogle Scholar
  4. 4.
    Barkoutsos, P.K., Nannicini, G., Robert, A., Tavernelli, I., Woerner, S.: Improving variational quantum optimization using CVaR. Quantum 4, 256 (2019)CrossRefGoogle Scholar
  5. 5.
    Beasley, J.E.: OR-library: distributing test problems by electronic mail. J. Oper. Res. Soc. 41(11), 1069–1072 (1990). http://www.jstor.org/stable/2582903
  6. 6.
    Beasley, J.: QUBO instances link - file bqpgka.txt. http://people.brunel.ac.uk/~mastjjb/jeb/orlib/bqpinfo.html
  7. 7.
    Benedetti, M., Lloyd, E., Sack, S., Fiorentini, M.: Parameterized quantum circuits as machine learning models. Quantum Sci. Technol. 4(4), 043001 (2019).  https://doi.org/10.1088/2058-9565/ab4eb5CrossRefGoogle Scholar
  8. 8.
    Beyer, H.: The theory of evolution strategies. In: Natural Computing Series. Springer, Berlin (2001).  https://doi.org/10.1007/978-3-662-04378-3
  9. 9.
    Booth, M., Reinhardt, S.P.: Partitioning optimization problems for hybrid classical/quantum execution technical report (2017)Google Scholar
  10. 10.
    Brandão, F.G.S.L., Broughton, M., Farhi, E., Gutmann, S., Neven, H.: For fixed control parameters the quantum approximate optimization algorithm’s objective function value concentrates for typical instances arXiv:1812.04170 (2018)
  11. 11.
    Bravyi, S., Gosset, D., König, R.: Quantum advantage with shallow circuits. Science 362(6412), 308–311 (2018).  https://doi.org/10.1126/science.aar3106, https://science.sciencemag.org/content/362/6412/308
  12. 12.
    Bravyi, S., Smith, G., Smolin, J.A.: Trading classical and quantum computational resources. Phys. Rev. X 6 (2016).  https://doi.org/10.1103/PhysRevX.6.021043, https://link.aps.org/doi/10.1103/PhysRevX.6.021043
  13. 13.
    Crooks, G.E.: Performance of the quantum approximate optimization algorithm on the maximum cut problem (2018). https://arxiv.org/abs/1811.08419
  14. 14.
    Doerr, B., Doerr, C.: Optimal static and self-adjusting parameter choices for the (1+(\(\lambda \), \(\lambda \))) genetic algorithm. Algorithmica 80(5), 1658–1709 (2018).  https://doi.org/10.1007/s00453-017-0354-9MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Doerr, B., Le, H.P., Makhmara, R., Nguyen, T.D.: Fast genetic algorithms. In: Bosman, P.A.N. (ed.) Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2017, Berlin, Germany, 15–19 July 2017, pp. 777–784. ACM (2017).  https://doi.org/10.1145/3071178.3071301
  16. 16.
    Doerr, C., Wang, H., Ye, F., van Rijn, S., Bäck, T.: IOHprofiler: a benchmarking and profiling tool for iterative optimization heuristics. arXiv e-prints:1810.05281, October 2018. https://arxiv.org/abs/1810.05281
  17. 17.
    Dunjko, V., Ge, Y., Cirac, J.I.: Computational speedups using small quantum devices. Phys. Rev. Lett. 121, 250501 (2018).  https://doi.org/10.1103/PhysRevLett.121.250501, https://link.aps.org/doi/10.1103/PhysRevLett.121.250501
  18. 18.
    Endo, S., Cai, Z., Benjamin, S.C., Yuan, X.: Hybrid quantum-classical algorithms and quantum error mitigation. J. Phys. Soc. Jpn. 90(3), 032001 (2020)CrossRefGoogle Scholar
  19. 19.
    Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm (2014)Google Scholar
  20. 20.
    Farhi, E., Harrow, A.W.: Quantum supremacy through the quantum approximate optimization algorithm (2016)Google Scholar
  21. 21.
    Glover, F., Hao, J.K.: Efficient evaluations for solving large 0–1 unconstrained quadratic optimisation problems. Int. J. Metaheuristics 1(1), 3–10 (2010).  https://doi.org/10.1504/IJMHEUR.2010.033120MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Glover, F., Kochenberger, G., Alidaee, B.: Adaptive memory tabu search for binary quadratic programs. Manage. Sci. 44, 336–345 (1998).  https://doi.org/10.1287/mnsc.44.3.336CrossRefzbMATHGoogle Scholar
  23. 23.
    Glover, F.W.: Tabu search. In: Handbook of Combinatorial Optimization, pp. 1537–1544. Springer, US, Boston, MA (2013).  https://doi.org/10.1007/978-1-4419-1153-7_1034
  24. 24.
    Glover, F.W., Lü, Z., Hao, J.K.: Diversification-driven tabu search for unconstrained binary quadratic problems. 4OR 8, 239–253 (2010)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Hansen, N.: Benchmarking a BI-population CMA-ES on the BBOB-2009 function testbed. In: ACM-GECCO Genetic and Evolutionary Computation Conference. Montreal, Canada, July 2009. https://hal.inria.fr/inria-00382093
  26. 26.
    Kandala, A., et al.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549, 242–246 (2017).  https://doi.org/10.1038/nature23879CrossRefGoogle Scholar
  27. 27.
    Kochenberger, G., et al.: The unconstrained binary quadratic programming problem: a survey. J. Comb. Optim. 28(1), 58–81 (2014).  https://doi.org/10.1007/s10878-014-9734-0MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Kochenberger, G.A., Glover, F.: A unified framework for modeling and solving combinatorial optimization problems: a tutorial. Multiscale Optim. Methods Appl. 101–124. Springer, US, Boston, MA (2006).  https://doi.org/10.1007/0-387-29550-X_4
  29. 29.
    Lehre, P.K., Yao, X.: Crossover can be constructive when computing unique input-output sequences. Soft. Comput. 15(9), 1675–1687 (2011)CrossRefGoogle Scholar
  30. 30.
    Li, L., Fan, M., Coram, M., Riley, P., Leichenauer, S.: Quantum optimization with a novel gibbs objective function and ansatz architecture search. Phys. Rev. Res. 2(2), 023074 (2019)CrossRefGoogle Scholar
  31. 31.
    Lü, Z., Glover, F.W., Hao, J.K.: A hybrid metaheuristic approach to solving the UBQP problem. Eur. J. Oper. Res. 207, 1254–1262 (2010)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Medvidovic, M., Carleo, G.: Classical variational simulation of the quantum approximate optimization algorithm (2020)Google Scholar
  33. 33.
    Moll, N., et al.: Quantum optimization using variational algorithms on near-term quantum devices. Quantum Sci. Technol. 3(3), 030503 (2018).  https://doi.org/10.1088/2058-9565/aab822CrossRefGoogle Scholar
  34. 34.
    Moussa, C., Calandra, H., Dunjko, V.: To quantum or not to quantum: towards algorithm selection in near-term quantum optimization. Quantum Sci. Technol. 5(4), 044009 (2020).  https://doi.org/10.1088/2058-9565/abb8e5CrossRefGoogle Scholar
  35. 35.
    Niko, A., Yoshihikoueno, Y., Brockhoff, D., Chan, M.: ARF1: CMA-ES/pycma: r3.0.3, April 2020.  https://doi.org/10.5281/zenodo.3764210
  36. 36.
    Palubeckis, G.: Multistart tabu search strategies for the unconstrained binary quadratic optimization problem. Ann. Oper. Res. 131, 259–282 (2004).  https://doi.org/10.1023/B:ANOR.0000039522.58036.68MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Palubeckis, G.: Iterated tabu search for the unconstrained binary quadratic optimization problem. Informatica (Vilnius) 17(2), 279–296 (2006)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Peng, T., Harrow, A.W., Ozols, M., Wu, X.: Simulating large quantum circuits on a small quantum computer. Phys. Rev. Lett. 125(15), 150504 (2020).  https://doi.org/10.1103/PhysRevLett.125.150504, https://link.aps.org/doi/10.1103/PhysRevLett.125.150504
  39. 39.
    Preskill, J.: Quantum Computing in the NISQ era and beyond. Quantum 2, 79 (2018).  https://doi.org/10.22331/q-2018-08-06-79CrossRefGoogle Scholar
  40. 40.
    Rennela, M., Laarman, A., Dunjko, V.: Hybrid divide-and-conquer approach for tree search algorithms (2020)Google Scholar
  41. 41.
    Rosenberg, G., Vazifeh, M., Woods, B., Haber, E.: Building an iterative heuristic solver for a quantum annealer. Comput. Optim. Appl. 65, 845–869 (2016)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Streif, M., Leib, M.: Comparison of QAOA with quantum and simulated annealing, arXiv:1901.01903 (2019)
  43. 43.
    Wang, Y., Lü, Z., Glover, F.W., Hao, J.K.: Path relinking for unconstrained binary quadratic programming. Eur. J. Oper. Res. 223, 595–604 (2012)MathSciNetCrossRefGoogle Scholar
  44. 44.
    Watson, R.A., Jansen, T.: A building-block royal road where crossover is provably essential. In: Proceeding of Genetic and Evolutionary Computation Conference (GECCO 2007), pp. 1452–1459. ACM (2007).  https://doi.org/10.1145/1276958.1277224
  45. 45.
    Willsch, M., Willsch, D., Jin, F., De Raedt, H., Michielsen, K.: Benchmarking the quantum approximate optimization algorithm. Quantum Inf. Process. 19(7), 197 (2020).  https://doi.org/10.1007/s11128-020-02692-8MathSciNetCrossRefGoogle Scholar
  46. 46.
    Zhou, L., Wang, S.T., Choi, S., Pichler, H., Lukin, M.D.: Quantum approximate optimization algorithm: performance, mechanism, and implementation on near-term devices, arXiv:1812.01041 (2018)

Copyright information

© Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.LIACSLeiden UniversityLeidenNetherlands
  2. 2.TOTAL SACourbevoieFrance

Personalised recommendations