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Quantum Program Synthesis: Swarm Algorithms and Benchmarks

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Genetic Programming (EuroGP 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11451))

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Abstract

In the two decades since Shor’s celebrated quantum algorithm for integer factorisation, manual design has failed to produce the anticipated growth in the number of quantum algorithms. Hence, there is a great deal of interest in the automatic synthesis of quantum circuits and algorithms. Here we present a set of experiments which use Ant Programming to automatically synthesise quantum circuits. In the proposed approach, ants choosing paths in high-dimensional Cartesian space are analogous to transformation of qubits in Hilbert space. In addition to the proposed algorithm, we introduce new evaluation criteria for searching the space of quantum circuits, both for classical simulation and simulation on a quantum computer. We demonstrate that the proposed approach significantly outperforms random search on a suite of benchmark problems based on these new measures.

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References

  1. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70(13), 1895–1899 (1993)

    Article  MathSciNet  Google Scholar 

  2. Brassard, G., Braunstein, S.L., Cleve, R.: Teleportation as a quantum computation. In: Proceedings of the Fourth Workshop on Physics and Computation, PhysComp 1996, pp. 43–47. Elsevier, Amsterdam (1998)

    Google Scholar 

  3. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press, Cambridge (2009)

    MATH  Google Scholar 

  4. Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. Roy. Soc. Lond. A 400(1818), 97–117 (1985)

    Article  MathSciNet  Google Scholar 

  5. Ding, S., Jin, Z., Yang, Q.: Evolving quantum circuits at the gate level with a hybrid quantum-inspired evolutionary algorithm. Soft Comput. 12(11), 1059–1072 (2008)

    Article  Google Scholar 

  6. Dorigo, M., Gambardella, L.M.: Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans. Evol. Comput. 1(1), 53–66 (1997)

    Article  Google Scholar 

  7. Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 26(1), 29–41 (1996)

    Article  Google Scholar 

  8. Fogel, L.J.: Autonomous automata. Ind. Res. 4, 14–19 (1962)

    Google Scholar 

  9. Gepp, A., Stocks, P.: A review of procedures to evolve quantum algorithms. Genet. Program. Evolvable Mach. 10(2), 181–228 (2009)

    Article  Google Scholar 

  10. Green, J., Whalley, J., Johnson, C.: Automatic programming with ant colony optimization. In: Proceedings of the 2004 UK Workshop on Computational Intelligence, pp. 70–77 (2004)

    Google Scholar 

  11. Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)

    Article  Google Scholar 

  12. Hales, L., Hallgren, S.: An improved quantum Fourier transform algorithm and applications. In: Proceedings of 41st Annual Symposium on Foundations of Computer Science, pp. 515–525. IEEE (2000)

    Google Scholar 

  13. Keber, C., Schuster, M.G.: Option valuation with generalized ant programming. In: Proceedings of the 4th Annual Conference on Genetic and Evolutionary Computation, pp. 74–81. Morgan Kaufmann Publishers Inc. (2002)

    Google Scholar 

  14. Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)

    MATH  Google Scholar 

  15. Leier, A., Banzhaf, W.: Evolving Hogg’s quantum algorithm using linear-tree GP. In: Cantú-Paz, E., et al. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 390–400. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-45105-6_48

    Chapter  Google Scholar 

  16. Lukac, M., et al.: Evolutionary approach to quantum and reversible circuits synthesis. Artif. Intell. Rev. 20(3–4), 361–417 (2003)

    Article  Google Scholar 

  17. Mann, H.B., Whitney, D.R.: On a test of whether one of two random variables is stochastically larger than the other. Ann. Math. Stat. 18(1), 50–60 (1947)

    Article  MathSciNet  Google Scholar 

  18. Massey, P., Clark, J.A., Stepney, S.: Evolving quantum circuits and programs through Genetic Programming. In: Deb, K. (ed.) GECCO 2004. LNCS, vol. 3103, pp. 569–580. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24855-2_66

    Chapter  Google Scholar 

  19. Massey, P., Clark, J.A., Stepney, S.: Human-competitive evolution of quantum computing artefacts by Genetic Programming. Evol. Comput. 14(1), 21–40 (2006)

    Article  Google Scholar 

  20. Miller, J.F.: An empirical study of the efficiency of learning Boolean functions using a Cartesian Genetic Programming approach. In: Proceedings of the 1st Annual Conference on Genetic and Evolutionary Computation - Volume 2, GECCO 1999, pp. 1135–1142. Morgan Kaufmann Publishers Inc., San Francisco (1999)

    Google Scholar 

  21. Nielsen, M.A., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  22. Reed, M., et al.: Realization of three-qubit quantum error correction with superconducting circuits. Nature 482(7385), 382–385 (2012)

    Article  Google Scholar 

  23. Roux, O., Fonlupt, C.: Ant programming: or how to use ants for automatic programming. In: Dorigo, M. (ed.) ANTS 2000 From Ant Colonies to Artificial Ants: 2nd International Workshop on Ant Algorithms (2000)

    Google Scholar 

  24. Shende, V.V., Markov, I.L.: On the CNOT-cost of TOFFOLI gates. Quantum Inf. Comput. 9(5), 461–486 (2009)

    MathSciNet  MATH  Google Scholar 

  25. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)

    Article  MathSciNet  Google Scholar 

  26. Spector, L., Barnum, H., Bernstein, H.J., Swamy, N.: Finding a better-than-classical quantum AND/OR algorithm using Genetic Programming. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC 1999, vol. 3, pp. 2239–2246. IEEE (1999)

    Google Scholar 

  27. Spector, L., Barnum, H., Bernstein, H.J., Swamy, N.: Quantum computing applications of Genetic Programming. Adv. Genet. program. 3, 135–160 (1999)

    Google Scholar 

  28. Spector, L., Klein, J.: Machine invention of quantum computing circuits by means of Genetic Programming. AI EDAM 22(3), 275–283 (2008)

    Google Scholar 

  29. Stadelhofer, R., Banzhaf, W., Suter, D.: Evolving blackbox quantum algorithms using Genetic Programming. AI EDAM 22(3), 285–297 (2008)

    Google Scholar 

  30. Stepney, S., Clark, J.A.: Searching for quantum programs and quantum protocols. J. Comput. Theor. Nanosci. 5(5), 942–969 (2008)

    Article  Google Scholar 

  31. Toffoli, T.: Reversible computing. In: de Bakker, J., van Leeuwen, J. (eds.) Automata, Languages and Programming. LNCS, vol. 85, pp. 632–644. Springer, Heidelberg (1980). https://doi.org/10.1007/3-540-10003-2_104

    Chapter  Google Scholar 

  32. Vargha, A., Delaney, H.D.: A critique and improvement of the CL common language effect size statistics of McGraw and Wong. J. Educ. Behav. Stat. 25(2), 101–132 (2000)

    Google Scholar 

  33. Williams, C.P., Gray, A.G.: Automated design of quantum circuits. In: Williams, C.P. (ed.) QCQC 1998. LNCS, vol. 1509, pp. 113–125. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-49208-9_8

    Chapter  Google Scholar 

  34. Yabuki, T., Iba, H.: Genetic algorithms for quantum circuit design - evolving a simpler teleportation circuit. In: Late Breaking Papers at the 2000 Genetic and Evolutionary Computation Conference, pp. 421–425. ACM (2000)

    Google Scholar 

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Acknowledgements

T. Atkinson and J. Swan acknowledge the support of EPSRC grant EP/J017515/1.

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Authors and Affiliations

  1. Department of Computer Science, University of York, York, UK

    Timothy Atkinson, Athena Karsa & Jerry Swan

  2. School of Electronic Engineering and Computer Science, Queen Mary University of London, London, UK

    John Drake

Authors
  1. Timothy Atkinson
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  2. Athena Karsa
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  3. John Drake
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  4. Jerry Swan
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Corresponding author

Correspondence to Timothy Atkinson .

Editor information

Editors and Affiliations

  1. Brno University of Technology, Brno, Czech Republic

    Lukas Sekanina

  2. Memorial University, St. John's, NL, Canada

    Ting Hu

  3. University of Coimbra, Coimbra, Portugal

    Nuno Lourenço

  4. HTWK Leipzig University of Applied Sciences, Leipzig, Germany

    Hendrik Richter

  5. University of Granada, Granada, Spain

    Pablo García-Sánchez

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Atkinson, T., Karsa, A., Drake, J., Swan, J. (2019). Quantum Program Synthesis: Swarm Algorithms and Benchmarks. In: Sekanina, L., Hu, T., Lourenço, N., Richter, H., García-Sánchez, P. (eds) Genetic Programming. EuroGP 2019. Lecture Notes in Computer Science(), vol 11451. Springer, Cham. https://doi.org/10.1007/978-3-030-16670-0_2

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  • DOI: https://doi.org/10.1007/978-3-030-16670-0_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-16669-4

  • Online ISBN: 978-3-030-16670-0

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