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Depth optimization for topological quantum circuits

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Abstract

Topological quantum computing (TQC) model is one of the most promising models for quantum computation. A circuit implemented under TQC is optimized by reducing its depth due to special construction requirements in such technology. In this work, we propose a hybrid approach that combines a left-edge greedy heuristic with genetic algorithm (GA) to minimize circuit depth through combined line and gate ordering. In our implementation, GA is used to find line ordering, whereas the left edge is used to reduce circuit depth by taking into consideration overlap constraints imposed by line ordering. Moreover, the proposed algorithm can merge gates together realizing circuit with multi-target gates to provide reduced circuit depth. Experimental results on random benchmark circuits show that the proposed algorithm was able to reduce circuit depth by 42 % on average for CNOT circuits, with additional 5 % savings when multi-target optimization is used. Results on RevLib benchmarks revealed a typical enhancement of 21 % and an additional 11 % when multi-target gates are allowed.

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References

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

    Google Scholar 

  2. Sarma, S.D., Freedman, M., Nayak, C.: Topological quantum computation. Phys. Today 59(7), 32–38 (2006)

  3. Fowler, A.G., Goyal, K.: Topological cluster state quantum computing. arXiv:0805.3202 [quant-ph] (2009)

  4. Devitt, S.J., Fowler, A.G., Stephens, A.M., Greentree, A.D., Hollenberg, L.C.L., Munro, W.J., Nemoto, K.: Architectural design for a topological cluster state quantum computer. New J. Phys. 11(8), 083032 (2009)

    Article  ADS  Google Scholar 

  5. Fowler, A.G., Stephens, A.M., Groszkowski, P.: High-threshold universal quantum computation on the surface code. Phys. Rev. A 80(5), 052312 (2009). (14 pages)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  7. Brown, B.J., Son, W., Kraus, C.V., Fazio, R., Vedral, V.: Generating topological order from a two-dimensional cluster state using a duality mapping. New J. Phys. 13(6), 065010 (2011)

  8. Fowler, A.G., Devitt, S.J.: A bridge to lower overhead quantum computation. arXiv preprint arXiv:1209.0510 (2012)

  9. Ohliger, M., Eisert, J.: Efficient measurement-based quantum computing with continuous-variable systems. Phys. Rev. A 85(6), 062318 (2012)

    Article  ADS  Google Scholar 

  10. Paler, A., Devitt, S.J., Nemoto, K., Polian, I.: Synthesis of topological quantum circuits. arXiv preprint arXiv:1302.5182 (2013)

  11. Alicea, J., Oreg, Y., Refael, G., von Oppen, F., Fisher, M.P.A.: Non-Abelian statistics and topological quantum information processing in 1D wire networks. Nat. Phys. 7, 412–417 (2011)

    Article  Google Scholar 

  12. Liu, X.-J., Wong, C.L.M., Law, K.T.: Non-abelian majorana doublets in time–reversal–invariant topological superconductors. Phys. Rev. X 4, 021018 (2014)

    Google Scholar 

  13. Nickerson, N.H., Li, Y., Benjamin, S.C.: Topological quantum computing with a very noisy network and local error rates approaching one percent. Nat. Commun. 4, 1756 (2013)

    Article  ADS  Google Scholar 

  14. Devitt, S., Nemoto, K.: Programming a topological quantum computer. In: Test Symposium (ATS), 2012 IEEE 21st Asian, pp. 55–60. IEEE (2012)

  15. Fowler, A.G.: Time-optimal quantum computation. arXiv preprint arXiv:1210.4626 (2012)

  16. 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)

    Article  ADS  Google Scholar 

  17. Jones, N.C., Van Meter, R., Fowler, A.G., McMahon, P.L., Kim, J., Ladd, T.D., Yamamoto, Y.: Layered architecture for quantum computing. Phys. Rev. X 2(3), 031007 (2012)

    Google Scholar 

  18. Abdessaied, N., Wille, R., Soeken, M., Drechsler, R.: Reducing the depth of quantum circuits using additional circuit lines. In: Proceedings of the 5th International Conference on Reversible Computation, RC’13, pp. 221–233. Springer, Berlin (2013)

  19. Drechsler, R., Wille, R.: Reversible circuits: recent accomplishments and future challenges for an emerging technology. In: Progress in VLSI Design and Test, pp. 383–392. Springer, Berlin (2012)

  20. Kerntopf, P., Perkowski, M., Podlaski, K.: Synthesis of reversible circuits: a view on the state-of-the-art. In: 12th IEEE Conference on Nanotechnology (IEEE-NANO), pp. 1–6 (2012)

  21. Saeedi, M., Markov, I.L.: Synthesis and optimization of reversible circuits–a survey. ACM Comput. Surv. 45(2), 21 (2013)

  22. Yamashita, S.: An optimization problem for topological quantum computation. In: IEEE 21st Asian Test Symposium (ATS), pp. 61–66. IEEE (2012)

  23. Bonesteel, N.E., Hormozi, L., Zikos, G., Simon, S.H.: Braid topologies for quantum computation. Phys. Rev. Lett. 95(14), 140503 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  24. Maslov, D., Dueck, G.W., Miller, D.M., Negrevergne, C.: Quantum circuit simplification and level compaction. IEEE Trans. Comput. Aid. Des. Integr. Circuits Syst. 27(3), 436–444 (2008)

    Article  Google Scholar 

  25. Arabzadeh, M., Saheb Zamani, M., Sedighi, M., Saeedi, M.: Depth-optimized reversible circuit synthesis. Quantum Inf. Process. 12(4), 1677–1699 (2013). ISSN 1570–0755

    Article  ADS  MATH  MathSciNet  Google Scholar 

  26. Bocharov, A., Svore, K.M.: A depth-optimal canonical form for single-qubit quantum circuits. Phys. Rev. Lett. 109, 190501 (2012). arXiv:1206.3223v1

  27. Amy, M., Maslov, D., Mosca, M., Roetteler, M.: A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits. IEEE Trans. Comput. Aid. Des. Integr. Circuits Syst. 32(6), 818–830 (2013)

    Article  Google Scholar 

  28. Wille, R., Lye, A., Drechsler, R.: Optimal swap gate insertion for nearest neighbor quantum circuits. In: ASP-DAC, pp. 489–494 (2014)

  29. Shafaei, A., Saeedi, M., Pedram, M.: Optimization of quantum circuits for interaction distance in linear nearest neighbor architectures. In: ACM Design Automation Conference (DAC-13), p. 41 (2013)

  30. Hirata, Y., Nakanishi, M., Yamashita, S., Nakashima, Y.: An efficient conversion of quantum circuits to a linear nearest neighbor architecture. Quantum Inf. Comput. 11(1), 142–166 (2011)

    MATH  MathSciNet  Google Scholar 

  31. Saeedi, M., Wille, R., Drechsler, R.: Synthesis of quantum circuits for linear nearest neighbor architectures. Quantum Inf. Process. 10(3), 355–377 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  32. Matsuo, A., Yamashita, S.: Changing the gate order for optimal lnn conversion. In: Proceedings of the Third International Conference on Reversible Computation, pp. 89–101 (2012)

  33. AlFailakawi, M., AlTerkawi, L., Ahmad, I., Hamdan, S.: Line ordering of reversible circuits for linear nearest neighbor realization. Quantum Inf. Process. 12(10), 3319–3339 (2013). ISSN 1570–0755

    Article  ADS  MATH  MathSciNet  Google Scholar 

  34. Hashimoto, A., Stevens, J.: Wire routing by optimizing channel assignment within large apertures. In: Proceedings of the 8th Design Automation Workshop, pp. 155–169. ACM (1971)

  35. Kurdahi, F.J., Parker, A.C.: Real: a program for register allocation. In: Proceedings of the 24th ACM/IEEE Design Automation Conference, pp. 210–215. ACM (1987)

  36. Wille, R., Soeken, M., Otterstedt, C., Drechsler, R.: Improving the mapping of reversible circuits to quantum circuits using multiple target lines. In: Design Automation Conference (ASP-DAC), 2013 18th Asia and South Pacific, pp. 145–150. IEEE (2013)

  37. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  38. Adam, T.L., Mani Chandy, K., Dickson, J.R.: A comparison of list schedules for parallel processing systems. Commun. ACM 17(12), 685–690 (1974)

    Article  MATH  Google Scholar 

  39. Wille, R., Grosse, D., Teuber, L., Dueck, G.W., Drechsler, R.: Revlib: An online resource for reversible functions and reversible circuits. In: 38th International Symposium on Multiple Valued Logic (ISMVL), pp. 220–225 (2008)

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Acknowledgments

The authors would like to thank Alexandru Paler and his team from the Faculty of Informatics and Mathematics, University of Passau-Germany for providing the tools for random circuit generation. Further, we would like to thank the anonymous reviewers for their invaluable comments which definitely improved overall quality of the manuscript.

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Authors and Affiliations

  1. Computer Engineering Department, College of Computing Sciences and Engineering, Kuwait University, Khaldiyah, Kuwait

    Mohammad AlFailakawi, Imtiaz Ahmad & Suha Hamdan

  2. Accounting and Management Information Systems Department, College of Business Administration, Gulf University of Science and Technology, Mishrif, Kuwait

    Laila AlTerkawi

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  1. Mohammad AlFailakawi
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  2. Imtiaz Ahmad
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  3. Laila AlTerkawi
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  4. Suha Hamdan
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Correspondence to Mohammad AlFailakawi.

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AlFailakawi, M., Ahmad, I., AlTerkawi, L. et al. Depth optimization for topological quantum circuits. Quantum Inf Process 14, 447–463 (2015). https://doi.org/10.1007/s11128-014-0867-y

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