NEASQC project
Published April 9, 2021 | Version v1
Conference paper Open

Tabu-Driven Quantum Neighborhood Samplers

Authors/Creators

  • 1. LIACS, Leiden University
  • 2. Total SA

Description

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.

Notes

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).

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Moussa2021_Chapter_Tabu-DrivenQuantumNeighborhood.pdf

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Additional details

Related works

Is part of
Book: 10.1007/978-3-030-72904-2 (DOI)
Book: 978-3-030-72903-5 (ISBN)

Funding

European Commission
NEASQC - NExt ApplicationS of Quantum Computing 951821

References

  • Arute, F., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505–510 (2019). https://doi.org/10.1038/s41586-019- 1666-5
  • Arute, F., et al.: Quantum approximate optimization of non-planar graph problems on a planar superconducting processor (2020)
  • Bäck, T.: Evolutionary Algorithms in Theory and Practice - Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford University Press, Oxford (1996)
  • Barkoutsos, P.K., Nannicini, G., Robert, A., Tavernelli, I., Woerner, S.: Improving variational quantum optimization using CVaR. Quantum 4, 256 (2019)
  • 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
  • Beasley, J.: QUBO instances link - file bqpgka.txt. http://people.brunel.ac.uk/ ~mastjjb/jeb/orlib/bqpinfo.html
  • 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/ab4eb5
  • Beyer, H.: The theory of evolution strategies. In: Natural Computing Series. Springer, Berlin (2001). https://doi.org/10.1007/978-3-662-04378-3
  • Booth, M., Reinhardt, S.P.: Partitioning optimization problems for hybrid classical/ quantum execution technical report (2017)
  • 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)
  • 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
  • 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
  • Crooks, G.E.: Performance of the quantum approximate optimization algorithm on the maximum cut problem (2018). https://arxiv.org/abs/1811.08419
  • Doerr, B., Doerr, C.: Optimal static and self-adjusting parameter choices for the (1+(λ, λ)) genetic algorithm. Algorithmica 80(5), 1658–1709 (2018). https://doi. org/10.1007/s00453-017-0354-9
  • 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
  • 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
  • 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
  • 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) C. Moussa et al.
  • Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm (2014)
  • Farhi, E., Harrow, A.W.: Quantum supremacy through the quantum approximate optimization algorithm (2016)
  • 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.2010.033120
  • 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.44.3.336
  • 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
  • Glover, F.W., Lü, Z., Hao, J.K.: Diversification-driven tabu search for unconstrained binary quadratic problems. 4OR 8, 239–253 (2010)
  • 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
  • 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/nature23879
  • 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/ s10878-014-9734-0
  • 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
  • Lehre, P.K., Yao, X.: Crossover can be constructive when computing unique inputoutput sequences. Soft. Comput. 15(9), 1675–1687 (2011)
  • 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)
  • 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)
  • Medvidovic, M., Carleo, G.: Classical variational simulation of the quantum approximate optimization algorithm (2020)
  • 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/aab822
  • 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/abb8e5
  • Niko, A., Yoshihikoueno, Y., Brockhoff, D., Chan, M.: ARF1: CMA-ES/pycma: r3.0.3, April 2020. https://doi.org/10.5281/zenodo.3764210
  • 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.0000039522.58036.68
  • Palubeckis, G.: Iterated tabu search for the unconstrained binary quadratic optimization problem. Informatica (Vilnius) 17(2), 279–296 (2006)
  • 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
  • Preskill, J.: Quantum Computing in the NISQ era and beyond. Quantum 2, 79 (2018). https://doi.org/10.22331/q-2018-08-06-79
  • Rennela, M., Laarman, A., Dunjko, V.: Hybrid divide-and-conquer approach for tree search algorithms (2020)
  • Rosenberg, G., Vazifeh, M., Woods, B., Haber, E.: Building an iterative heuristic solver for a quantum annealer. Comput. Optim. Appl. 65, 845–869 (2016)
  • Streif, M., Leib, M.: Comparison of QAOA with quantum and simulated annealing, arXiv:1901.01903 (2019)
  • 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)
  • 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
  • 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/s11128-020-02692-8
  • Zhou, L., Wang, S.T., Choi, S., Pichler, H., Lukin, M.D.: Quantum approximate optimization algorithm: performance, mechanism, and implementation on nearterm devices, arXiv:1812.01041 (2018)