On Post-processing the Results of Quantum Optimizers

  • Ajinkya BorleEmail author
  • Josh McCarter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11934)


The use of quantum computing for applications involving optimization has been regarded as one of the areas it may prove to be advantageous (against classical computation). To further improve the solutions, post-processing techniques are often used on the results of quantum optimization. One such recent approach is the Multi Qubit Correction (MQC) algorithm by Dorband. In this paper, we will discuss and analyze the strengths and weaknesses of this technique. Based on our discussion, we perform an experiment on (i) how pairing heuristics on the input of MQC can affect the results of a quantum optimizer and (ii) a comparison between MQC and the built-in optimization method that D-wave Systems offers. Among our results, we are able to show that the built-in post-processing rarely beats MQC in our tests. We hope that by using the ideas and insights presented in this paper, researchers and developers will be able to make a more informed decision on what kind of post-processing methods to use for their quantum optimization needs.


Quantum optimization Quantum annealing Approximation Evolutionary algorithm D-wave QAOA 



We would like to thank John Dorband, Milton Halem and Samuel Lomonaco, Helmut Katzgraber and Nicholas Chancellor for their feedback. A special thanks to D-wave Systems for providing us access to their machines.


  1. 1.
    The d-wave post-processing documentation.
  2. 2.
    Adachi, S.H., Henderson, M.P.: Application of quantum annealing to training of deep neural networks. arXiv preprint arXiv:1510.06356 (2015)
  3. 3.
    Dorband, J.E.: Stochastic characteristics of qubits and qubit chains on the D-wave 2X. arXiv preprint arXiv:1606.05550 (2016)
  4. 4.
    Dorband, J.E.: A method of finding a lower energy solution to a qubo/ising objective function. arXiv preprint arXiv:1801.04849 (2018)
  5. 5.
    Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028 (2014)
  6. 6.
    Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Quantum computation by adiabatic evolution. arXiv preprint quant-ph/0001106 (2000)Google Scholar
  7. 7.
    Gallavotti, G.: Statistical Mechanics: A Short Treatise. Springer, Heidelberg (2013)zbMATHGoogle Scholar
  8. 8.
    Greenwood, G.W.: Finding solutions to NP problems: philosophical differences between quantum and evolutionary search algorithms. In: Proceedings of the 2001 Congress on Evolutionary Computation, vol. 2, pp. 815–822. IEEE (2001)Google Scholar
  9. 9.
    Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325 (1997)CrossRefGoogle Scholar
  10. 10.
    Harris, R., et al.: Phase transitions in a programmable quantum spin glass simulator. Science 361(6398), 162–165 (2018)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Houdayer, J.: A cluster Monte Carlo algorithm for 2-dimensional spin glasses. Eur. Phys. J. B-Condens. Matter Complex Syst. 22(4), 479–484 (2001)CrossRefGoogle Scholar
  12. 12.
    Jensen, F.V.: Bayesian updating in causal probabilistic networks by local computations. An introduction to Bayesian networks (1996)Google Scholar
  13. 13.
    Kadowaki, T., Nishimori, H.: Quantum annealing in the transverse ising model. Phys. Rev. E 58(5), 5355 (1998)CrossRefGoogle Scholar
  14. 14.
    Karimi, H., Rosenberg, G.: Boosting quantum annealer performance via sample persistence. Quantum Inf. Process. 16(7), 166 (2017)CrossRefGoogle Scholar
  15. 15.
    Karimi, H., Rosenberg, G., Katzgraber, H.G.: Effective optimization using sample persistence: a case study on quantum annealers and various monte carlo optimization methods. Phys. Rev. E 96(4), 043312 (2017)CrossRefGoogle Scholar
  16. 16.
    Katzgraber, H.G., Hamze, F., Andrist, R.S.: Glassy chimeras could be blind to quantum speedup: designing better benchmarks for quantum annealing machines. Phys. Rev. X 4(2), 021008 (2014)Google Scholar
  17. 17.
    Markowitz, H.M.: The elimination form of the inverse and its application to linear programming. Manag. Sci. 3(3), 255–269 (1957)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Neukart, F., Compostella, G., Seidel, C., von Dollen, D., Yarkoni, S., Parney, B.: Traffic flow optimization using a quantum annealer. Front. ICT 4, 29 (2017)CrossRefGoogle Scholar
  19. 19.
    Ochoa, A.J., Jacob, D.C., Mandrà, S., Katzgraber, H.G.: Feeding the multitude: a polynomial-time algorithm to improve sampling. Phys. Rev. E 99(4), 043306 (2019)CrossRefGoogle Scholar
  20. 20.
    O’Malley, D.: An approach to quantum-computational hydrologic inverse analysis. Sci. Rep. 8(1), 6919 (2018)MathSciNetCrossRefGoogle Scholar
  21. 21.
    O’Malley, D., Vesselinov, V.V., Alexandrov, B.S., Alexandrov, L.B.: Nonnegative/binary matrix factorization with a d-wave quantum annealer. PLoS One 13(12), e0206653 (2018)CrossRefGoogle Scholar
  22. 22.
    Peruzzo, A., et al.: A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5, 4213 (2014)CrossRefGoogle Scholar
  23. 23.
    Preskill, J.: Quantum computing in the NISQ era and beyond. arXiv preprint arXiv:1801.00862 (2018)
  24. 24.
    Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: 1994 Proceedings of 35th Annual Symposium on Foundations of Computer Science, pp. 124–134. IEEE (1994)Google Scholar
  25. 25.
    Tanaka, S., Tamura, R., Chakrabarti, B.K.: Quantum Spin Glasses. Annealing and Computation. Cambridge University Press, Cambridge (2017)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.CSEE DepartmentUniversity of Maryland Baltimore CountyBaltimoreUSA

Personalised recommendations