Skip to main content
SpringerLink
Log in

A design method for efficient variational quantum models based on specific Pauli axis

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

The combination of quantum computing and machine learning is expected to solve problems that cannot be realized by classical computers in machine learning. In current quantum machine learning, variational quantum algorithm is the mainstream quantum models, and classical neural networks are replaced by parameterized quantum gates. In the noisy-intermediate scale quantum computer, it is important to design lightweight and efficient quantum networks. This paper proposes a method for designing parameterized quantum circuits based on specific Pauli axis. By obtaining the prior information of the coding strategy, using the rotational characteristics of the quantum gate to reasonably combine the quantum gate and efficiently realize the classification task on a specific Pauli axis, it can reduce the amount of parameters in the variational quantum circuit. In addition, considering the current topology of quantum computers, the design method of circuit entanglement structure is given. Finally, the performance is compared with two general-purpose models on four low-dimensional datasets, and the circuit designed in this paper has fewer parameters and faster convergence speed. In addition, the three models are simulated with noise, and the test set is predicted on the Rigetti Aspen-M-3 quantum computer.

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
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

Data availability

All code, dataset and other accessible materials in this article can be obtained through the email address of the corresponding author.

References

  1. Lau, J.W.Z., Lim, K.H., Shrotriya, H., Kwek, L.C.: NISQ computing: where are we and where do we go? AAPPS Bull. 32(1), 27 (2022)

    Article  ADS  Google Scholar 

  2. Schuld, M., Killoran, N.: Is quantum advantage the right goal for quantum machine learning? Prx Quantum 3(3), 030101 (2022)

    Article  ADS  Google Scholar 

  3. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 212–219 (1996)

  4. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Ostaszewski, M., Grant, E., Benedetti, M.: Structure optimization for parameterized quantum circuits. Quantum 5, 391 (2021)

    Article  Google Scholar 

  6. Zhu, D., Linke, N.M., Benedetti, M., Landsman, K.A., Nguyen, N.H., Alderete, C.H., Perdomo-Ortiz, A., Korda, N., Garfoot, A., Brecque, C., et al.: Training of quantum circuits on a hybrid quantum computer. Sci. Adv. 5(10), 9918 (2019)

    Article  ADS  Google Scholar 

  7. Benedetti, M., Lloyd, E., Sack, S., Fiorentini, M.: Parameterized quantum circuits as machine learning models. Quantum Sci. Technol. 4(4), 043001 (2019)

    Article  ADS  Google Scholar 

  8. Farhi, E., Goldstone, J., Gutmann, S., Neven, H.: Quantum algorithms for fixed qubit architectures (2017). arXiv preprint arXiv:1703.06199

  9. Gyongyosi, L., Imre, S.: State stabilization for gate-model quantum computers. Quantum Inf. Process. 18, 24 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  10. Maronese, M., Destri, C., Prati, E.: Quantum activation functions for quantum neural networks. Quantum Inf. Process. 21(4), 128 (2022)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Benedetti, M., Grant, E., Wossnig, L., Severini, S.: Adversarial quantum circuit learning for pure state approximation. New J. Phys. 21(4), 043023 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  12. Schuld, M., Petruccione, F., Schuld, M., Petruccione, F.: Variational circuits as machine learning models. Mach. Learn. Quantum Comput. 24, 177–215 (2021)

    MATH  Google Scholar 

  13. Khairy, S., Shaydulin, R., Cincio, L., Alexeev, Y., Balaprakash, P.: Learning to optimize variational quantum circuits to solve combinatorial problems. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 34, pp. 2367–2375 (2020)

  14. Li, T., Xu, Z., Li, F.: Wireless broadband signal detection scheme based on quantum machine learning. J. Signal Process. 17, 9–39 (2023)

    ADS  Google Scholar 

  15. Schuld, M.: Supervised quantum machine learning models are kernel methods (2021). arXiv preprint arXiv:2101.11020

  16. Henry, L.-P., Thabet, S., Dalyac, C., Henriet, L.: Quantum evolution kernel: machine learning on graphs with programmable arrays of qubits. Phys. Rev. A 104(3), 032416 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  17. Schuld, M., Killoran, N.: Quantum machine learning in feature Hilbert spaces. Phys. Rev. Lett. 122(4), 040504 (2019)

    Article  ADS  Google Scholar 

  18. Blank, C., Park, D.K., Rhee, J.-K.K., Petruccione, F.: Quantum classifier with tailored quantum kernel. Npj Quantum Inf. 6(1), 41 (2020)

    Article  ADS  Google Scholar 

  19. Burgholzer, L., Schneider, S., Wille, R.: Limiting the search space in optimal quantum circuit mapping. In: 2022 27th Asia and South Pacific Design Automation Conference (ASP-DAC), pp. 466–471 (2022). IEEE

  20. Periyasamy, M., Meyer, N., Ufrecht, C., Scherer, D.D., Plinge, A., Mutschler, C.: Incremental data-uploading for full-quantum classification. In: 2022 IEEE International Conference on Quantum Computing and Engineering (QCE), pp. 31–37 (2022). IEEE

  21. Rakyta, P., Zimborás, Z.: Approaching the theoretical limit in quantum gate decomposition. Quantum 6, 710 (2022)

    Article  Google Scholar 

  22. Bhattacharjee, D., Saki, A.A., Alam, M., Chattopadhyay, A., Ghosh, S.: Muqut: multi-constraint quantum circuit mapping on nisq computers. In: 2019 IEEE/ACM International Conference on Computer-Aided Design (ICCAD), pp. 1–7 (2019). IEEE

  23. Preskill, J.: Quantum computing in the nisq era and beyond. Quantum 2, 79 (2018)

    Article  Google Scholar 

  24. Coyle, B.: Machine learning applications for noisy intermediate-scale quantum computers (2022). arXiv preprint arXiv:2205.09414

  25. Bharti, K., Cervera-Lierta, A., Kyaw, T., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J., Menke, T., et al.: Noisy intermediate-scale quantum (nisq) algorithms (2021). arXiv preprint arXiv:2101.08448

  26. Díez-Valle, P., Porras, D., García-Ripoll, J.J.: Quantum variational optimization: the role of entanglement and problem hardness. Phys. Rev. A 104(6), 062426 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  27. Schuld, M., Sweke, R., Meyer, J.J.: Effect of data encoding on the expressive power of variational quantum-machine-learning models. Phys. Rev. A 103(3), 032430 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  28. Pérez-Salinas, A., Cervera-Lierta, A., Gil-Fuster, E., Latorre, J.I.: Data re-uploading for a universal quantum classifier. Quantum 4, 226 (2020)

    Article  Google Scholar 

  29. Lloyd, S., Schuld, M., Ijaz, A., Izaac, J., Killoran, N.: Quantum embeddings for machine learning (2020). arXiv preprint arXiv:2001.03622

  30. Ostaszewski, M., Trenkwalder, L.M., Masarczyk, W., Scerri, E., Dunjko, V.: Reinforcement learning for optimization of variational quantum circuit architectures. Adv. Neural. Inf. Process. Syst. 34, 18182–18194 (2021)

    Google Scholar 

  31. Meng, F.-X., Li, Z.-T., Yu, X.-T., Zhang, Z.-C.: Quantum circuit architecture optimization for variational quantum eigensolver via Monto Carlo tree search. IEEE Trans. Quantum Eng. 2, 1–10 (2021)

    Article  Google Scholar 

  32. Bergholm, V., Izaac, J., Schuld, M., Gogolin, C., Ahmed, S., Ajith, V., Alam, M.S., Alonso-Linaje, G., AkashNarayanan, B., Asadi, A., et al.: Pennylane: Automatic differentiation of hybrid quantum-classical computations (2018). arXiv preprint arXiv:1811.04968

  33. Havlíček, V., Córcoles, A.D., Temme, K., Harrow, A.W., Kandala, A., Chow, J.M., Gambetta, J.M.: Supervised learning with quantum-enhanced feature spaces. Nature 567(7747), 209–212 (2019)

    Article  ADS  Google Scholar 

  34. Suzuki, Y., Yano, H., Gao, Q., Uno, S., Tanaka, T., Akiyama, M., Yamamoto, N.: Analysis and synthesis of feature map for kernel-based quantum classifier. Quantum Mach. Intell. 2, 1–9 (2020)

    Article  Google Scholar 

  35. Huang, H.-Y., Kueng, R., Preskill, J.: Information-theoretic bounds on quantum advantage in machine learning. Phys. Rev. Lett. 126(19), 190505 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  36. Chen, S., Cotler, J.S., Huang, H.-Y., Li, J.Z.: Exponential separations between learning with and without quantum memory. In: 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS), pp. 574–585 (2021)

  37. Huang, H.-Y., Broughton, M., Cotler, J.S., Chen, S., Li, J.Z., Mohseni, M., Neven, H., Babbush, R., Kueng, R., Preskill, J., McClean, J.R.: Quantum advantage in learning from experiments. Science 376, 1182–1186 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  38. Huang, H.-Y., Kueng, R., Preskill, J.: Predicting many properties of a quantum system from very few measurements. Nat. Phys. 25, 1–8 (2020)

    Google Scholar 

  39. Sim, S., Johnson, P.D., Aspuru-Guzik, A.: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Adv. Quantum Technol. 2(12), 1900070 (2019)

    Article  Google Scholar 

  40. Li, G., Ye, R., Zhao, X., Wang, X.: Concentration of data encoding in parameterized quantum circuits (2022). arXiv preprint arXiv:2206.08273

Download references

Acknowledgements

Resources and computing environment provided by Nanjing University of Posts and Telecommunications, Nanjing, China, thanks to the support of the school.

Funding

This work is supported by National Natural Science Foundation of China under Grants Nos. 62271265 and 62271266.

Author information

Author notes

  1. Bowen Li and Ting Li have made equal contributions.

Authors and Affiliations

  1. Nanjing University of Posts and Telecommunications, Nanjing, 210003, Jiangsu Province, China

    Bowen Li, Ting Li & Fei Li

Authors
  1. Bowen Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ting Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the conception and design of the study. The methodology and experiments are operated by BL. The refinement of the manuscript was carried out by TL and FL. The funding was applied for by TL, and all authors commented on previous manuscripts. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Ting Li.

Ethics declarations

Conflict of interest

All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or nonfinancial interest in the subject matter or materials discussed in this manuscript.

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

Li, B., Li, T. & Li, F. A design method for efficient variational quantum models based on specific Pauli axis. Quantum Inf Process 22, 387 (2023). https://doi.org/10.1007/s11128-023-04127-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-04127-6

Keywords

Search

Navigation