Skip to main content
SpringerLink
Log in

A dynamic programming approach to multi-objective logic synthesis of quantum circuits

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Quantum computing is an emerging technology that harnesses the laws of quantum mechanics to solve some problems much faster than classical computers. Quantum-logic synthesis refers to converting a given quantum gate into a set of gates that can be implemented in quantum technologies and primarily focuses on decreasing the number of CNOT gates. Of the most well-known quantum-logic synthesis methods are cosine-sine decomposition (CSD) and quantum Shannon decomposition (QSD), each with their distinct advantages. This study aims to present a multi-objective quantum-logic synthesis to optimize three evaluation criteria of the synthesized circuit, namely, the number of CNOT gates, the total number of gates, and the depth simultaneously. The proposed method involves constructing a solution space by exploring various combinations of CSD and QSD. Then, utilizing a bottom-up approach of multi-objective dynamic programming (MODP), a method is presented to search only a specific part of the entire solution space to find circuits with Pareto-optimal costs, i.e., the Pareto-optimal front. The results obtained from this method demonstrate a balance between the evaluation criteria. Furthermore, many Pareto-optimal solutions are generated that can be considered based on the applications’ or the quantum technology requirements.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Algorithm 1
Algorithm 2

Similar content being viewed by others

Data Availability

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. Moore, G.E.: Cramming more components onto integrated circuits. Proc. IEEE 86(1), 82–85 (1998)

    Article  Google Scholar 

  2. Williams, C.P.: Explorations in Quantum Computing. Texts in Computer Science. Springer, London (2010)

    Google Scholar 

  3. Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52(5), 3457 (1995)

    Article  ADS  Google Scholar 

  4. Bullock, S.S., Markov, I.L.: Asymptotically optimal circuits for arbitrary \(n\)-qubit diagonal computations. Quantum Inf. Comput. 4(1), 27–47 (2004)

    MathSciNet  MATH  Google Scholar 

  5. Saeedi, M., Arabzadeh, M., Zamani, M.S., Sedighi, M.: Block-based quantum-logic synthesis. Quantum Inf. Comput. J. 11(3), 262–277 (2010)

    MathSciNet  MATH  Google Scholar 

  6. Shende, V.V., Bullock, S.S., Markov, I.L.: Synthesis of quantum-logic circuits. IEEE Trans. CAD 25(6), 1000–1010 (2006)

    Article  Google Scholar 

  7. Lee, S., Lee, S.-J., Kim, T., Lee, J.-S., Biamonte, J., Perkowski, M.: The cost of quantum gate primitives. J. Multip. Valued Logic Soft Comput. 12, 561–573 (2006)

    MathSciNet  MATH  Google Scholar 

  8. Saeedi, M., Markov, I.L.: Synthesis and optimization of reversible circuits—a survey. ACM Comput. Surv. (CSUR) 45(2), 1–34 (2013)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  12. Bennett, C.H.: Quantum cryptography: public key distribution and coin tossing. In: Proceeding of IEEE International Conference on Computer System and Signal Processing New York, pp. 175–179 (1984)

  13. Cybenko, G.: Reducing quantum computations to elementary unitary operations. Comput. Sci. Eng. 3(2), 27–32 (2001)

    Article  Google Scholar 

  14. Shende, V.V., Markov, I.L., Bullock, S.S.: Minimal universal two-qubit controlled-not-based circuits. Phys. Rev. A 69(6), 062321 (2004)

    Article  ADS  Google Scholar 

  15. Möttönen, M., Vartiainen, J.J., Bergholm, V., Salomaa, M.M.: Quantum circuits for general multiqubit gates. Phys. Rev. Lett. 93(13), 130502 (2004)

    Article  ADS  Google Scholar 

  16. Bergholm, V., Vartiainen, J.J., Möttönen, M., Salomaa, M.M.: Quantum circuits with uniformly controlled one-qubit gates. Phys. Rev. A 71, 052330 (2005)

    Article  ADS  MATH  Google Scholar 

  17. Vidal, G., Dawson, C.M.: Universal quantum circuit for two-qubit transformations with three controlled-not gates. Phys. Rev. A 69(1), 010301 (2004)

    Article  ADS  Google Scholar 

  18. Shende, V.V., Markov, I.L., Bullock, S.S.: Smaller two-qubit circuits for quantum communication and computation, vol. 2, pp. 980–985 (2004)

  19. Vatan, F., Williams, C.: Optimal quantum circuits for general two-qubit gates. Phys. Rev. A 69(3), 032315 (2004)

    Article  ADS  Google Scholar 

  20. Song, G., Klappenecker, A.: Optimal realizations of controlled unitary gates. Quantum Inf. Comput. 3(2), 139–155 (2003)

    MathSciNet  MATH  Google Scholar 

  21. Arabzadeh, M., Houshmand, M., Sedighi, M., Zamani, M.S.: Quantum-logic synthesis of Hermitian gates. ACM J. Emerg. Technol. Comput. Syst. (JETC) 12(4), 1–15 (2015)

    Google Scholar 

  22. Houshmand, M., Zamani, M.S., Sedighi, M., Arabzadeh, M.: Decomposition of diagonal Hermitian quantum gates using multiple-controlled pauli Z gates. ACM J. Emerg. Technol. Comput. Syst. (JETC) 11(3), 1–10 (2014)

    Article  Google Scholar 

  23. Danos, V., Kashefi, E., Panangaden, P., Perdrix, S.: Extended measurement calculus. Semantic techniques in quantum computation, pp. 235–310 (2009)

  24. Houshmand, M., Sedighi, M., Zamani, M.S., Marjoei, K.: Quantum circuit synthesis targeting to improve one-way quantum computation pattern cost metrics. ACM J. Emerg. Technol. Comput. Syst. (JETC) 13(4), 1–27 (2017)

    Article  Google Scholar 

  25. Steane, A.M.: Error correcting codes in quantum theory. Phys. Rev. Lett. 77(5), 793 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Bacon, D.: Operator quantum error-correcting subsystems for self-correcting quantum memories. Phys. Rev. A 73(1), 012340 (2006)

    Article  ADS  Google Scholar 

  27. Wang, D.S., Fowler, A.G., Hollenberg, L.C.L.: Surface code quantum computing with error rates over 1%. Phys. Rev. A 83(2), 020302 (2011)

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  29. Lin, C.-C., Chakrabarti, A., Jha, N.K.: FTQLS: fault-tolerant quantum logic synthesis. IEEE Trans. Very Large Scale Integr. VLSI Syst. 22(6), 1350–1363 (2013)

    Article  Google Scholar 

  30. 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)

    MathSciNet  Google Scholar 

  31. Giles, B., Selinger, P.: Exact synthesis of multiqubit Clifford+ T circuits. Phys. Rev. A 87(3), 032332 (2013)

    Article  ADS  Google Scholar 

  32. Häner, T., Soeken, M.: Lowering the T-depth of quantum circuits via logic network optimization. ACM Trans. Quantum Comput. 3(2), 1–15 (2022)

    Article  MathSciNet  Google Scholar 

  33. Hwang, Y.: Fault-tolerant circuit synthesis for universal fault-tolerant quantum computing (2022). arXiv preprint arXiv:2206.02691

  34. Krol, A.M., Sarkar, A., Ashraf, I., Al-Ars, Z., Bertels, K.: Efficient decomposition of unitary matrices in quantum circuit compilers. Appl. Sci. 12(2), 759 (2022)

    Article  Google Scholar 

  35. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2011). (10th anniversary edition edition)

    MATH  Google Scholar 

  36. Dawson, C.M., Nielsen, M.A.: The Solovay–Kitaev algorithm. Quantum Inf. Comput. 6(1), 81–95 (2006)

    MathSciNet  MATH  Google Scholar 

  37. Kliuchnikov, V., Maslov, D., Mosca, M.: Asymptotically optimal approximation of single qubit unitaries by Clifford and T circuits using a constant number of ancillary qubits. Phys. Rev. Lett. 110(19), 190502 (2013)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    Arezoo Rajaei & Mahboobeh Houshmand

  2. Department of Electrical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    Seyyed Abed Hosseini

Authors
  1. Arezoo Rajaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mahboobeh Houshmand
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Seyyed Abed Hosseini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mahboobeh Houshmand.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rajaei, A., Houshmand, M. & Hosseini, S.A. A dynamic programming approach to multi-objective logic synthesis of quantum circuits. Quantum Inf Process 22, 384 (2023). https://doi.org/10.1007/s11128-023-04112-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-04112-z

Keywords

Search

Navigation