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Quantum Information Processing

, Volume 14, Issue 1, pp 1–36 | Cite as

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

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

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.

Keywords

Quantum computation Quantum annealing keyword  Operational planning 

Notes

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.

References

  1. 1.
    Rieffel, E.G., Polak, W.: A Gentle Introduction to Quantum Computing. MIT Press, Cambridge, MA (2011)Google Scholar
  2. 2.
    Nielsen, M., Chuang, I.L.: Quantum Computing and Quantum Information. Cambridge University Press, Cambridge (2001)Google Scholar
  3. 3.
    Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Quantum computation by adiabatic evolution. arXiv:quant-ph/0001106 (2000)
  4. 4.
    Das, A., Chakrabarti, B.K.: Colloquium: quantum annealing and analog quantum computation. Rev. Mod. Phys. 80, 1061 (2008)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  5. 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. 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)ADSCrossRefGoogle Scholar
  7. 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. 8.
    Smolin, J.A., Smith, G.: Classical signature of quantum annealing. arXiv:1305.4904 (2013)
  9. 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. 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)CrossRefGoogle Scholar
  11. 11.
    Shin, S.W., Smith, G., Smolin, J.A., Vazirani, U.: How “quantum” is the D-Wave machine? arXiv:1401.7087 (2014)
  12. 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. 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. 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)Google Scholar
  15. 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. 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)Google Scholar
  17. 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)Google Scholar
  18. 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. 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. 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. 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. 22.
    Babbush, R., Love, P.J., Aspuru-Guzik, A.: Adiabatic quantum simulation of quantum chemistry. arXiv:1311.3967 (2013)
  23. 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)Google Scholar
  24. 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. 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. 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. 27.
    Ghallab, M., Nau, D., Traverso, P.: Automated Planning: Theory and Practice. Elsevier, Amsterdam (2004)Google Scholar
  28. 28.
    Long, D., Fox, M.: PDDL2. 1: an extension to PDDL for expressing temporal planning domains. J. Artif. Intell. Res. 20, 1 (2003)CrossRefzbMATHGoogle Scholar
  29. 29.
    Helmert, M.: Complexity results for standard benchmark domains in planning. Artifi. Intell. J. 143(2), 219–262 (2003)Google Scholar
  30. 30.
    Hoffmann, J.: Local search topology in planning benchmarks: an empirical analysis. J. Artif. Intell. Res. 24, 685 (2005)zbMATHGoogle Scholar
  31. 31.
    Komlós, J., Szemerédi, E.: Limit distribution for the existence of Hamiltonian cycles in a random graph. Discrete Math. 43(1), 55 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  32. 32.
    Cheeseman, P., Kanefsky, B., Taylor, W.M.: Where the really hard problems are. IJCAI 91, 331–337 (1991)Google Scholar
  33. 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)Google Scholar
  34. 34.
    Achlioptas, D., Friedgut, E.: A sharp threshold for k-colorability. Random Struct. Algorithm. 14(1), 63 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  35. 35.
    Coja-Oghlan, A.: Upper-bounding the k-colorability threshold by counting covers. arXiv:1305.0177 (2013)
  36. 36.
    Achlioptas, D., Moore, C.: Almost all graphs with average degree 4 are 3-colorable. J. Comput. Syst. Sci. 67(2), 441 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  37. 37.
    Dubois, O., Mandler, J.: On the non-3-colourability of random graphs. arXiv:math/0209087 (2002)
  38. 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)Google Scholar
  39. 39.
    Choi, V.: Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design. Quantum Inf. Process. 7(5), 193 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  40. 40.
    Lucas, A.: Ising formulations of many NP problems. arXiv:1302.5843 (2013)
  41. 41.
    Blum, A., Furst, M.: Fast planning through planning graph analysis. Artif. Intell. J. 90, 281 (1997)CrossRefzbMATHGoogle Scholar
  42. 42.
    Kautz, H.: Working Notes on the Fourth International Planning Competition (IPC-2004) pp. 44–45 (2004)Google Scholar
  43. 43.
    Boros, E., Hammer, P.L.: Pseudo-boolean optimization. Discrete Appl. Math. 123(1), 155 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  44. 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)CrossRefzbMATHMathSciNetGoogle Scholar
  45. 45.
    Klymko, C., Sullivan, B.D., Humble, T.S.: Adiabatic quantum programming: minor embedding with hard faults. Quantum Inf. Process. 13(3), 709 (2014)CrossRefzbMATHMathSciNetGoogle Scholar
  46. 46.
    Cai, J., Macready, B., Roy, A.: A practical heuristic for finding graph minors. arXiv:1406.2741 (2014)
  47. 47.
    Pudenz, K.L., Albash, T., Lidar, D.A.: Error-corrected quantum annealing with hundreds of qubits. Nat. Commun. (2014). doi: 10.1038/ncomms4243

Copyright information

© Springer Science+Business Media New York (outside the USA)  2014

Authors and Affiliations

  • Eleanor G. Rieffel
    • 1
  • Davide Venturelli
    • 1
  • Bryan O’Gorman
    • 1
  • Minh B. Do
    • 1
  • Elicia M. Prystay
    • 1
  • Vadim N. Smelyanskiy
    • 1
  1. 1.NASA Ames Research CenterMoffett FieldUSA

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