Greedy Randomized Search for Scalable Compilation of Quantum Circuits

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10848)


This paper investigates the performances of a greedy randomized algorithm to optimize the realization of nearest-neighbor compliant quantum circuits. Current technological limitations (decoherence effect) impose that the overall duration (makespan) of the quantum circuit realization be minimized. One core contribution of this paper is a lexicographic two-key ranking function for quantum gate selection: the first key acts as a global closure metric to minimize the solution makespan; the second one is a local metric acting as “tie-breaker” for avoiding cycling. Our algorithm has been tested on a set of quantum circuit benchmark instances of increasing sizes available from the recent literature. We demonstrate that our heuristic approach outperforms the solutions obtained in previous research against the same benchmark, both from the CPU efficiency and from the solution quality standpoint.


Quantum computing Optimization Scheduling Planning Greedy heuristics Random algorithms 


  1. 1.
    Hart, J., Shogan, A.: Semi-greedy heuristics: an empirical study. Oper. Res. Lett. 6, 107–114 (1987)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Resende, M.G., Werneck, R.F.: A hybrid heuristic for the p-median problem. J. Heuristics 10(1), 59–88 (2004)CrossRefGoogle Scholar
  3. 3.
    Oddi, A., Smith, S.: Stochastic procedures for generating feasible schedules. In: Proceedings 14th National Conference on AI (AAAI-1997), pp. 308–314 (1997)Google Scholar
  4. 4.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition, 10th edn. Cambridge University Press, New York (2011)zbMATHGoogle Scholar
  5. 5.
    Cirac, J.I., Zoller, P.: Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995)CrossRefGoogle Scholar
  6. 6.
    Herrera-Martí, D.A., Fowler, A.G., Jennings, D., Rudolph, T.: Photonic implementation for the topological cluster-state quantum computer. Phys. Rev. A 82, 032332 (2010)CrossRefGoogle Scholar
  7. 7.
    Yao, N.Y., Gong, Z.X., Laumann, C.R., Bennett, S.D., Duan, L.M., Lukin, M.D., Jiang, L., Gorshkov, A.V.: Quantum logic between remote quantum registers. Phys. Rev. A 87, 022306 (2013)CrossRefGoogle Scholar
  8. 8.
    Brierley, S.: Efficient implementation of quantum circuits with limited qubit interactions. arXiv preprint arXiv:1507.04263, September 2016
  9. 9.
    Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028, November 2014
  10. 10.
    Guerreschi, G.G., Park, J.: Gate scheduling for quantum algorithms. arXiv preprint arXiv:1708.00023, July 2017
  11. 11.
    Sete, E.A., Zeng, W.J., Rigetti, C.T.: A functional architecture for scalable quantum computing. In: 2016 IEEE International Conference on Rebooting Computing (ICRC), pp. 1–6, October 2016Google Scholar
  12. 12.
    Venturelli, D., Do, M., Rieffel, E., Frank, J.: Temporal planning for compilation of quantum approximate optimization circuits. In: Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI-2017, pp. 4440–4446 (2017)Google Scholar
  13. 13.
    Maslov, D., Falconer, S.M., Mosca, M.: Quantum circuit placement: optimizing qubit-to-qubit interactions through mapping quantum circuits into a physical experiment. In: Proceedings of the 44th Annual Design Automation Conference, DAC 2007, pp. 962–965. ACM, New York (2007)Google Scholar
  14. 14.
    Fox, M., Long, D.: PDDL2.1: An extension to PDDL for expressing temporal planning domains. J. Artif. Int. Res. 20(1), 61–124 (2003)zbMATHGoogle Scholar
  15. 15.
    Nau, D., Ghallab, M., Traverso, P.: Automated Planning: Theory & Practice. Morgan Kaufmann Publishers Inc., San Francisco (2004)zbMATHGoogle Scholar
  16. 16.
    Kole, A., Datta, K., Sengupta, I.: A heuristic for linear nearest neighbor realization of quantum circuits by swap gate insertion using \(n\)-gate lookahead. IEEE J. Emerg. Sel. Top. Circ. Syst. 6(1), 62–72 (2016)CrossRefGoogle Scholar
  17. 17.
    Kole, A., Datta, K., Sengupta, I.: A new heuristic for \(n\) -dimensional nearest neighbor realization of a quantum circuit. IEEE Trans. Comput.-Aided Des. Integr. Circ. Syst. 37(1), 182–192 (2018)CrossRefGoogle Scholar
  18. 18.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)zbMATHGoogle Scholar
  19. 19.
    Gomes, C.P., Selman, B., Kautz, H.: Boosting combinatorial search through randomization. In: Proceedings of the Fifteenth National/Tenth Conference on Artificial Intelligence/Innovative Applications of Artificial Intelligence. AAAI 1998/IAAI 1998, pp. 431–437. American Association for Artificial Intelligence, Menlo Park (1998)Google Scholar
  20. 20.
    Eyerich, P., Mattmüller, R., Röger, G.: Using the context-enhanced additive heuristic for temporal and numeric planning. In: Proceedings of the 19th International Conference on Automated Planning and Scheduling, ICAPS 2009, Thessaloniki, Greece, 19–23 September 2009 (2009)Google Scholar
  21. 21.
    Wah, B.W., Chen, Y.: Subgoal partitioning and global search for solving temporal planning problems in mixed space. Int. J. Artif. Intell. Tools 13(04), 767–790 (2004)CrossRefGoogle Scholar
  22. 22.
    Chen, Y., Wah, B.W., Hsu, C.W.: Temporal planning using subgoal partitioning and resolution in SGPlan. J. Artif. Int. Res. 26(1), 323–369 (2006)zbMATHGoogle Scholar
  23. 23.
    Gerevini, A., Saetti, A., Serina, I.: Planning through stochastic local search and temporal action graphs in LPG. J. Artif. Int. Res. 20(1), 239–290 (2003)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Cognitive Sciences and Technologies (ISTC-CNR)RomeItaly

Personalised recommendations