Skip to main content
SpringerLink
Log in

A case study in programming a quantum annealer for hard operational planning problems

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We report on a case study in programming an early quantum annealer to attack optimization problems related to operational planning. While a number of studies have looked at the performance of quantum annealers on problems native to their architecture, and others have examined performance of select problems stemming from an application area, ours is one of the first studies of a quantum annealer’s performance on parametrized families of hard problems from a practical domain. We explore two different general mappings of planning problems to quadratic unconstrained binary optimization (QUBO) problems, and apply them to two parametrized families of planning problems, navigation-type and scheduling-type. We also examine two more compact, but problem-type specific, mappings to QUBO, one for the navigation-type planning problems and one for the scheduling-type planning problems. We study embedding properties and parameter setting and examine their effect on the efficiency with which the quantum annealer solves these problems. From these results, we derive insights useful for the programming and design of future quantum annealers: problem choice, the mapping used, the properties of the embedding, and the annealing profile all matter, each significantly affecting the performance.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Rieffel, E.G., Polak, W.: A Gentle Introduction to Quantum Computing. MIT Press, Cambridge, MA (2011)

    Google Scholar 

  2. Nielsen, M., Chuang, I.L.: Quantum Computing and Quantum Information. Cambridge University Press, Cambridge (2001)

    Google Scholar 

  3. Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Quantum computation by adiabatic evolution. arXiv:quant-ph/0001106 (2000)

  4. Das, A., Chakrabarti, B.K.: Colloquium: quantum annealing and analog quantum computation. Rev. Mod. Phys. 80, 1061 (2008)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. Smelyanskiy, V.N., Rieffel, E.G., Knysh, S.I., Williams, C.P., Johnson, M.W., Thom, M.C., Macready, W.G., Pudenz, K.L.: A near-term quantum computing approach for hard computational problems in space exploration. arXiv:1204.2821 (2012)

  6. Johnson, M., Amin, M., Gildert, S., Lanting, T., Hamze, F., Dickson, N., Harris, R., Berkley, A., Johansson, J., Bunyk, P., et al.: Quantum annealing with manufactured spins. Nature 473(7346), 194 (2011)

    Article  ADS  Google Scholar 

  7. Boixo, S., Albash, T., Spedalieri, F.M., Chancellor, N., Lidar, D.A.: Experimental signature of programmable quantum annealing. Nat. Commun. (2013). doi:10.1038/ncomms3067

  8. Smolin, J.A., Smith, G.: Classical signature of quantum annealing. arXiv:1305.4904 (2013)

  9. Wang, L., Rønnow, T.F., Boixo, S., Isakov, S.V., Wang, Z., Wecker, D., Lidar, D.A., Martinis, J.M., Troyer, M.: Comment on “Classical signature of quantum annealing”. arXiv:1305.5837 (2013)

  10. Boixo, S., Rønnow, T.F., Isakov, S.V., Wang, Z., Wecker, D., Lidar, D.A., Martinis, J.M., Troyer, M.: Evidence for quantum annealing with more than one hundred qubits. Nat. Phys. 10(3), 218 (2014)

    Article  Google Scholar 

  11. Shin, S.W., Smith, G., Smolin, J.A., Vazirani, U.: How “quantum” is the D-Wave machine? arXiv:1401.7087 (2014)

  12. Vinci, W., Albash, T., Mishra, A., Warburton, P.A., Lidar, D.A.: Distinguishing classical and quantum models for the D-Wave device. arXiv:1403.4228 (2014)

  13. Shin, S.W., Smith, G., Smolin, J.A., Vazirani, U.: Comment on “Distinguishing classical and quantum models for the D-Wave device”. arXiv:1404.6499 (2014)

  14. Rieffel, E.G., Venturelli, D., Hen, I., Do, M., Frank, J.: Parametrized families of hard planning problems from phase transitions. In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence (AAAI-14), pp. 2337–2343,(2014)

  15. Wang, Z., Boixo, S., Albash, T., Lidar, D.: Benchmarking the D-Wave adiabatic quantum optimizer via 2D-Ising spin glasses. APS Meeting Abstr. 1, 27005 (2013)

    Google Scholar 

  16. Rønnow, T.F., Wang, Z., Job, J., Boixo, S., Isakov, S.V., Wecker,D., Martinis, J.M., Lidar, D.A., Troyer, M.: Defining and detectingquantum speedup. Science 345(6195), 420 (2014)

  17. Wang, Z., Job, J., Troyer, M., Lidar, D.A. et al.: Performance of quantum annealing on random Ising problems implemented using the D-wave two. Bull. Am. Phys. Soc. (2014)

  18. Venturelli, D., Mandra, S., Knysh, S., OGorman, B., Biswas, R., Smelyanskiy, V.: Quantum optimization of fully-connected spin glasses. arXiv:1406.7553 (2014)

  19. Kassal, I., Whitfield, J.D., Perdomo-Ortiz, A., Yung, M.H., Aspuru-Guzik, A.: Simulating chemistry using quantum computers. arXiv:1007.2648 (2010)

  20. Perdomo-Ortiz, A., Dickson, N., Drew-Brook, M., Rose, G., Aspuru-Guzik, A.: Finding low-energy conformations of lattice protein models by quantum annealing. Sci. Rep. (2012). doi:10.1038/srep00571

  21. Babbush, R., Perdomo-Ortiz, A., O’Gorman, B., Macready, W., Aspuru-Guzik, A.: Construction of energy functions for lattice heteropolymer models: a case study in constraint satisfaction programming and adiabatic quantum optimization. arXiv:1211.3422 (2012)

  22. Babbush, R., Love, P.J., Aspuru-Guzik, A.: Adiabatic quantum simulation of quantum chemistry. arXiv:1311.3967 (2013)

  23. Perdomo-Ortiz, A., Fluegemann, J., Narasimhan, S., Smelyanskiy, V., Biswas, R.: A quantum approach to diagnosis of multiple faults in electrical power systems. In: 5th IEEE International Conference on Space Mission Challenges for Information Technology. (To appear.) (2014)

  24. O’Gorman, B., Perdomo-Ortiz, A., Babbush, R., Aspuru-Guzik, A., Smelyanskiy, V.: Bayesian network structure learning using quantum annealing. Eur. Phys. J. Spec. Top. arXiv:1407.3897 (2014)

  25. Perdomo-Ortiz, A., Fluegemann, J., Narasimhan, S., Biswas, R., Smelyanskiy, V.: Programming and solving real-world applications on a quantum annealing device. arXiv:1406.7601 (2014)

  26. Fikes, R.E., Nilsson, N.J.: STRIPS: a new approach to the application of theorem proving to problem solving. Artif. Intell. 2(3), 189 (1972)

    Google Scholar 

  27. Ghallab, M., Nau, D., Traverso, P.: Automated Planning: Theory and Practice. Elsevier, Amsterdam (2004)

    Google Scholar 

  28. Long, D., Fox, M.: PDDL2. 1: an extension to PDDL for expressing temporal planning domains. J. Artif. Intell. Res. 20, 1 (2003)

    Article  MATH  Google Scholar 

  29. Helmert, M.: Complexity results for standard benchmark domains in planning. Artifi. Intell. J. 143(2), 219–262 (2003)

  30. Hoffmann, J.: Local search topology in planning benchmarks: an empirical analysis. J. Artif. Intell. Res. 24, 685 (2005)

    MATH  Google Scholar 

  31. Komlós, J., Szemerédi, E.: Limit distribution for the existence of Hamiltonian cycles in a random graph. Discrete Math. 43(1), 55 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  32. Cheeseman, P., Kanefsky, B., Taylor, W.M.: Where the really hard problems are. IJCAI 91, 331–337 (1991)

  33. Chien, S., Johnston, M., Frank, J., Giuliano, M., Kavelaars, A., Lenzen, C., Policella, N., Verfailie, G.: A generalized timeline representation, services, and interface for automating space mission operations. In: 12th International Conference on Space Operations (2012)

  34. Achlioptas, D., Friedgut, E.: A sharp threshold for k-colorability. Random Struct. Algorithm. 14(1), 63 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  35. Coja-Oghlan, A.: Upper-bounding the k-colorability threshold by counting covers. arXiv:1305.0177 (2013)

  36. Achlioptas, D., Moore, C.: Almost all graphs with average degree 4 are 3-colorable. J. Comput. Syst. Sci. 67(2), 441 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  37. Dubois, O., Mandler, J.: On the non-3-colourability of random graphs. arXiv:math/0209087 (2002)

  38. Culberson, J., Beacham, A., Papp, D.: Hiding our colors. In: Proceedings of the CP95 Workshop on Studying and Solving Really Hard Problems, pp. 31–42, (1995)

  39. Choi, V.: Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design. Quantum Inf. Process. 7(5), 193 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  40. Lucas, A.: Ising formulations of many NP problems. arXiv:1302.5843 (2013)

  41. Blum, A., Furst, M.: Fast planning through planning graph analysis. Artif. Intell. J. 90, 281 (1997)

    Article  MATH  Google Scholar 

  42. Kautz, H.: Working Notes on the Fourth International Planning Competition (IPC-2004) pp. 44–45 (2004)

  43. Boros, E., Hammer, P.L.: Pseudo-boolean optimization. Discrete Appl. Math. 123(1), 155 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  44. Babbush, R., O’Gorman, B., Aspuru-Guzik, A.: Resource efficient gadgets for compiling adiabatic quantum optimization problems. Ann. Phys. 525(10–11), 877 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  45. Klymko, C., Sullivan, B.D., Humble, T.S.: Adiabatic quantum programming: minor embedding with hard faults. Quantum Inf. Process. 13(3), 709 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  46. Cai, J., Macready, B., Roy, A.: A practical heuristic for finding graph minors. arXiv:1406.2741 (2014)

  47. Pudenz, K.L., Albash, T., Lidar, D.A.: Error-corrected quantum annealing with hundreds of qubits. Nat. Commun. (2014). doi:10.1038/ncomms4243

Download references

Acknowledgments

The authors are grateful to Jeremy Frank, Alejandro Perdomo-Ortiz, Sergey Knysh, Itay Hen, Ross Beyer, and Chris Henze for helpful discussions, and to D-Wave for technical support and for discussions related to the calibration issue and our results before and after. This work was supported in part by the Office of the Director of National Intelligence (ODNI), the Intelligence Advanced Research Projects Activity (IARPA), via IAA 145483; by the AFRL Information Directorate under grant F4HBKC4162G001. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of ODNI, IARPA, AFRL, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purpose notwithstanding any copyright annotation thereon. The authors also would like to acknowledge support from the NASA Advanced Exploration Systems program and NASA Ames Research Center.

Author information

Authors and Affiliations

  1. NASA Ames Research Center, Moffett Field, CA, 94025, USA

    Eleanor G. Rieffel, Davide Venturelli, Bryan O’Gorman, Minh B. Do, Elicia M. Prystay & Vadim N. Smelyanskiy

Authors
  1. Eleanor G. Rieffel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Davide Venturelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bryan O’Gorman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Minh B. Do
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Elicia M. Prystay
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Vadim N. Smelyanskiy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eleanor G. Rieffel.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rieffel, E.G., Venturelli, D., O’Gorman, B. et al. A case study in programming a quantum annealer for hard operational planning problems. Quantum Inf Process 14, 1–36 (2015). https://doi.org/10.1007/s11128-014-0892-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-014-0892-x

Keywords

Search

Navigation