Advertisement

Synthesizing Quantum Circuits via Numerical Optimization

  • Timothée Goubault de BrugièreEmail author
  • Marc Baboulin
  • Benoît Valiron
  • Cyril Allouche
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11537)

Abstract

We provide a simple framework for the synthesis of quantum circuits based on a numerical optimization algorithm. This algorithm is used in the context of the trapped-ions technology. We derive theoretical lower bounds for the number of quantum gates required to implement any quantum algorithm. Then we present numerical experiments with random quantum operators where we compute the optimal parameters of the circuits and we illustrate the correctness of the theoretical lower bounds. We finally discuss the scalability of the method with the number of qubits.

Keywords

Quantum circuit synthesis Numerical optimization Quantum simulation Quantum circuit optimization Trapped-ions technology 

Notes

Acknowledgement

This work was supported in part by the French National Research Agency (ANR) under the research project SoftQPRO ANR-17-CE25-0009-02, and by the DGE of the French Ministry of Industry under the research project PIA-GDN/QuantEx P163746-484124.

References

  1. 1.
    Arrazola, J.M., Bromley, T.R., Izaac, J., Myers, C.R., Bradler, K., Killoran, N.: Machine learning method for state preparation and gate synthesis on photonic quantum computers. Quantum Science and Technology (2018)Google Scholar
  2. 2.
    Bravyi, S., Browne, D., Calpin, P., Campbell, E., Gosset, D., Howard, M.: Simulation of quantum circuits by low-rank stabilizer decompositions. arXiv preprint arXiv:1808.00128 (2018)
  3. 3.
    Giles, B., Selinger, P.: Exact synthesis of multiqubit clifford+\(t\) circuits. Phys. Rev. A 87, 032332 (2013)CrossRefGoogle Scholar
  4. 4.
    Goubault de Brugière, T., Baboulin, M., Valiron, B., Allouche, C.: Quantum circuits synthesis using householder transformations (2018, submitted)Google Scholar
  5. 5.
    Graham, A.: Kronecker Products and Matrix Calculus with Application. Wiley, New York (1981)zbMATHGoogle Scholar
  6. 6.
    Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing, STOC 1996, pp. 212–219. ACM, New York (1996)Google Scholar
  7. 7.
    Guillemin, V., Pollack, A.: Differential Topology, vol. 370. American Mathematical Society (2010)Google Scholar
  8. 8.
    Harrow, A.W., Hassidim, A., Lloyd, S.: Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103, 150502 (2009)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Kerenidis, I., Prakash, A.: Quantum recommendation systems. In: Papadimitriou, C.H. (ed.) 8th Innovations in Theoretical Computer Science Conference, ITCS 2017. LIPIcs, vol. 67, pp. 49:1–49:21. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2017)Google Scholar
  10. 10.
    Kliuchnikov, V., Maslov, D., Mosca, M.: Fast and efficient exact synthesis of single-qubit unitaries generated by Clifford and T gates. Quantum Inf. Comput. 13(7–8), 607–630 (2013)MathSciNetGoogle Scholar
  11. 11.
    Knill, E.: Approximation by quantum circuits. arXiv preprint arXiv:quant-ph/9508006 (1995)
  12. 12.
    Li, R., Alvarez-Rodriguez, U., Lamata, L., Solano, E.: Approximate quantum adders with genetic algorithms: an IBM quantum experience. arXiv preprint arXiv:1611.07851 (2016)
  13. 13.
    Lukac, M., et al.: Evolutionary approach to quantum and reversible circuits synthesis. Artif. Intell. Rev. 20(3–4), 361–417 (2003)CrossRefGoogle Scholar
  14. 14.
    Martinez, E.A., Monz, T., Nigg, D., Schindler, P., Blatt, R.: Compiling quantum algorithms for architectures with multi-qubit gates. New J. Phys. 18(6), 063029 (2016)CrossRefGoogle Scholar
  15. 15.
    Mottonen, M., Vartiainen, J.J.: Decompositions of general quantum gates. arXiv preprint arXiv:quant-ph/0504100 (2005)
  16. 16.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2011)zbMATHGoogle Scholar
  17. 17.
    Plesch, M., Brukner, Č.: Quantum-state preparation with universal gate decompositions. Phys. Rev. A 83, 032302 (2011)CrossRefGoogle Scholar
  18. 18.
    Preskill, J.: Quantum Computing in the NISQ era and beyond. Quantum 2, 79 (2018)CrossRefGoogle Scholar
  19. 19.
    Python: Scientific computing tools for Python (SciPy). https://www.scipy.org
  20. 20.
    Shende, V.V., Bullock, S.S., Markov, I.L.: Synthesis of quantum-logic circuits. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 25(6), 1000–1010 (2006)CrossRefGoogle Scholar
  21. 21.
    Shende, V.V., Markov, I.L., Bullock, S.S.: Minimal universal two-qubit controlled-not-based circuits. Phys. Rev. A 69(6), 062321 (2004)CrossRefGoogle Scholar
  22. 22.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Stewart, G.: The efficient generation of random orthogonal matrices with an application to condition estimators. SIAM J. Numer. Anal. 17(3), 403–409 (1980)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Vidal, G.: Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett. 91, 147902 (2003)CrossRefGoogle Scholar
  25. 25.
    Wright, S., Nocedal, J.: Numerical optimization. Science 35(67–68), 7 (1999)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Timothée Goubault de Brugière
    • 1
    • 3
    • 4
    Email author
  • Marc Baboulin
    • 1
    • 3
  • Benoît Valiron
    • 2
    • 3
  • Cyril Allouche
    • 4
  1. 1.University of Paris-SudOrsayFrance
  2. 2.CentraleSupélecGif sur YvetteFrance
  3. 3.Laboratoire de Recherche en InformatiqueOrsayFrance
  4. 4.Atos Quantum LabLes Clayes-sous-BoisFrance

Personalised recommendations