Skip to main content
SpringerLink
Log in

Quantum annealing learning search for solving QUBO problems

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, we present a novel strategy to solve optimization problems within a hybrid quantum-classical scheme based on quantum annealing, with a particular focus on QUBO problems. The proposed algorithm implements an iterative structure where the representation of an objective function into the annealer architecture is learned and already visited solutions are penalized by a tabu-inspired search. The result is a heuristic search equipped with a learning mechanism to improve the encoding of the problem into the quantum architecture. We prove the convergence of the algorithm to a global optimum in the case of general QUBO problems. Our technique is an alternative to the direct reduction of a given optimization problem into the sparse annealer graph.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. Namely, the elements \(\{a_{ij}\}\) of A satisfy: \(a_{ij}\ge 0\) \(\forall i,j\) and \(\sum _{j} a_{ij}=1\) \(\forall i\).

  2. G is strongly connected if for any pair of vertices \(x_i\) and \(x_j\) there is a direct path connecting them.

References

  1. Abbott, A.A., Calude, C.S., Dinneen, M.J., Hua, R.: A hybrid quantum-classical paradigm to mitigate embedding costs in quantum annealing. (2018). CoRR, abs/1803.04340

  2. Anily, S., Federgruen, A.: Ergodicity in parametric non-stationary Markov chains: applications to simulated annealing methods. Oper. Res. 35(6), 867–874 (1987)

    Article  MathSciNet  Google Scholar 

  3. Anily, S., Federgruen, A.: Simulated annealing methods with general acceptance probabilities. J. Appl. Probab. 24, 657–667 (1987)

    Article  MathSciNet  Google Scholar 

  4. 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: Proc. FroCoS 2017—The 11th International Symposium on Frontiers of Combining Systems LNCS, Springer (2017)

  5. Corporate Headquarters D-wave problem-solving handbook (2018)

  6. Das, A., Chakrabarti, B.K.: Quantum annealing and related optimization methods Springer Lecture Notes in Physics 679 (2005)

  7. Faigle, U., Kern, W.: Note on the convergence of simulated annealing algorithms. SIAM J. Control Optim. 29, 153–159 (1991)

    Article  MathSciNet  Google Scholar 

  8. Faigle, U., Kern, W.: Some convergence results for probabilistic tabu search. ORSA J. Comput. 4(1), 32–37 (1992)

    Article  Google Scholar 

  9. Glover, F.: Tabu search–part 1. ORSA J. Comput. 1(3), 190–206 (1989)

    Article  MathSciNet  Google Scholar 

  10. Glover, F.: Tabu search–part 2. ORSA J. Comput. 2(1), 4–32 (1990)

    Article  MathSciNet  Google Scholar 

  11. Häggström, O.: Finite Markov chains and algorithmic applications. In: London Mathematical Society Student Texts. Cambridge University Press, Cambridge, pp. 23–27 (2002)

  12. Johnson, M.W.: Future hardware directions of quantum annealing. Qubits Europe 2018, D-Wave Users Conference (2018)

  13. Kadowaki, T., Nishimori, H.: Quantum annealing in the transverse Ising model. Phys. Rev. E 58, 5355 (1998)

    Article  ADS  Google Scholar 

  14. McGeoch, C.C.: Adiabatic quantum computation and quantum annealing: theory and practice. Synth. Lect. Quantum Comput. (2014). https://doi.org/10.2200/S00585ED1V01Y201407QMC008

    Article  Google Scholar 

  15. Morita, S., Nishimori, H.: Mathematical foundation of quantum annealing. J. Math. Phys. (2008). https://doi.org/10.1063/1.2995837

    Article  MathSciNet  MATH  Google Scholar 

  16. Rosenberg, G., Vazifeh, M., Woods, B., Haber, E.: Building an iterative heuristic solver for a quantum annealer. Comput. Optim. Appl. 65(3), 845–869 (2016)

    Article  MathSciNet  Google Scholar 

  17. Tran, T.T., Do, M., Rieffel, E.G., Frank, J., Wang, Z., O’Gorman, B., Venturelli, D., Beck, J.C.: A hybrid quantum-classical approach to solving scheduling problems. In: Ninth Annual Symposium on Combinatorial Search (2016)

Download references

Acknowledgements

The authors are grateful to the anonymous referee for substantial suggestions and useful comments and to Roberto Sebastiani and Margherita Zorzi for providing feedback on a preliminary version of the paper. This work is supported by Fondazione Caritro.

Author information

Author notes

  1. Davide Pastorello and Enrico Blanzieri have contributed equally.

Authors and Affiliations

  1. Department of Mathematics, University of Trento, Trento Institute for Fundamental Physics and Applications, via Sommarive 14, 38123, Povo (Trento), Italy

    Davide Pastorello

  2. Department of Engineering and Computer Science, University of Trento, via Sommarive 9, 38123, Povo (Trento), Italy

    Enrico Blanzieri

Authors
  1. Davide Pastorello
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Enrico Blanzieri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Davide Pastorello.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pastorello, D., Blanzieri, E. Quantum annealing learning search for solving QUBO problems. Quantum Inf Process 18, 303 (2019). https://doi.org/10.1007/s11128-019-2418-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-019-2418-z

Keywords

Search

Navigation