Skip to main content
SpringerLink
Log in

Hybrid scheme for factorisation: Factoring 551 using a 3-qubit NMR quantum adiabatic processor

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

Quantum processors are potentially superior to their classical counterparts for many computational tasks including factorisation. Circuit methods as well as adiabatic methods have already been proposed and implemented for finding the factors of a given composite number. The main challenge in scaling it to larger numbers is the unavailability of large number of qubits. Here, we propose a hybrid scheme that involves both classical and quantum computation, based on the previous work of Peng et al, Phys. Rev. Lett. 101(22), 220405 (2008), which reduces the number of qubits required for factorisation. The classical part involves setting up and partially simplifying a set of bit-wise factoring equations and the quantum part involves solving these coupled equations using a quantum adiabatic process. We demonstrate the hybrid scheme by factoring 551 using a 3-qubit NMR quantum register.

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

Similar content being viewed by others

References

  1. N Koblitz, A course in number theory and cryptography (Springer, New York, 1994) Vol. 114

  2. P W Shor, Proc. 35th Annual Symposium on Foundations of Computer Science (IEEE Computer Society Press, Los Alatimos, CA, 1994) pp. 124–134

  3. P W Shor, SIAM Rev. 41(2), 303 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  4. L  M K Vandersypen, M Steffen, G Breyta, C S Yannoni, M H Sherwood and I L Chuang, Nature 414(6866), 883 (2001)

    Article  ADS  Google Scholar 

  5. C-Y Lu, D E Browne, T Yang and J-W Pan, Phys. Rev. Lett. 99, 250504 (2007)

    Article  ADS  Google Scholar 

  6. T Monz, D Nigg, E A Martinez, M F Brandl, P Schindler, R Rines, S X Wang, I L Chuang and R Blatt, Science 351(6277), 1068 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  7. M A Nielsen and I L Chuang, Quantum computation and quantum information (Cambridge University Press, Cambridge, 2010)

  8. X Peng, Z Liao, N Xu, G Qin, X Zhou, D Suter and J Du, Phys. Rev. Lett. 101(22), 220405 (2008)

    Article  ADS  Google Scholar 

  9. N Xu, J Zhu, D Lu, X Zhou, X Peng and J Du, Phys. Rev. Lett. 108(13), 130501 (2012)

    Article  ADS  Google Scholar 

  10. N S Dattani and N Bryans, Quantum factorization of 56153 with only 4 qubits, arXiv preprint arXiv:1411.6758 (2014)

  11. E Farhi, J Goldstone, S Gutmann, J Lapan, A Lundgren and D Preda, Science 292(5516), 472 (2001)

    Google Scholar 

  12. H Hu et al Phys. Rev. A 93(1), 012345 (2016)

  13. A Messiah, Quantum mechanics (North-Holland, Amsterdam, 1962) Vol. 2

  14. A Mitra, T S Mahesh and A Kumar, J. Chem. Phys. 128(12), 124110 (2008)

    Article  ADS  Google Scholar 

  15. J Cavanagh, W J Fairbrother, A G Palmer III and N J Skelton, Protein NMR spectroscopy: Principles and practice (Academic Press, San Diego, 1995)

  16. M H Levitt, Spin dynamics: Basics of nuclear magnetic resonance (Wiley-VCH, Chichester, 2001)

  17. D G Cory, M D Price and T F Havel, Phys. D: Nonlinear Phenom. 120(1), 82 (1998)

    Article  ADS  Google Scholar 

  18. E Knill, I Chuang and R Laflamme, Phys. Rev. A 57, 3348 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  19. J R Samal, A K Pati and A Kumar, Phys. Rev. Lett. 106, 080401 (2011)

    Article  ADS  Google Scholar 

  20. G Bhole, V S Anjusha and T S Mahesh, Phys. Rev. A 93, 042339 (2016)

    Article  ADS  Google Scholar 

  21. J A Jones, S D Karlen, J Fitzsimons, A Ardavan, S C Benjamin, G A D Briggs and J J L Morton, Science 324(5931), 1166 (2009)

    Article  ADS  Google Scholar 

  22. I L Chuang, N Gershenfeld, M G Kubinec and D W Leung, Proc. R. Soc. London A: Math. Phys. Eng. Sci. 454, 447 (1998)

    Article  ADS  Google Scholar 

  23. R Das, T S Mahesh and A Kumar, Phys. Rev. A 67(6), 062304 (2003)

    Article  ADS  Google Scholar 

  24. A M Childs, E Farhi and J Preskill, Phys. Rev. A 65, 012322 (2001)

    Article  ADS  Google Scholar 

  25. W Van Dam, M Mosca and U Vazirani, Proceedings of the 42nd Symposium on Foundations of Computer Science (IEEE, Los Alatimos, 2001) pp. 279–287

Download references

Acknowledgements

The authors acknowledge the useful discussions with Sudheer Kumar and Abhishek Shukla. SP and SM acknowledge the hospitality from Indian Institute of Science where this work was initiated. SM would like to thank Indian Academy of Sciences for the support during this period. This work was supported by the Department of Science and Technology, India (Grant Number DST / SJF / PSA-03 / 2012-13) and Council of Scientific and Industrial Research, India (Grant Number CSIR-03(1345) / 16 / EMR-II).

Author information

Authors and Affiliations

  1. Department of Physics, Indian Institute of Science Education and Research, Pashan, 411 008, India

    Soham Pal, V S Anjusha & T S Mahesh

  2. SISSA – International School for Advanced Studies, via Bonomea 265, 34136 , Trieste, Italy

    Saranyo Moitra

  3. Department of Physics and NMR Research Centre, Indian Institute of Science, Bengaluru, 560 012, India

    Anil Kumar

Authors
  1. Soham Pal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saranyo Moitra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V S Anjusha
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Anil Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. T S Mahesh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Soham Pal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pal, S., Moitra, S., Anjusha, V.S. et al. Hybrid scheme for factorisation: Factoring 551 using a 3-qubit NMR quantum adiabatic processor. Pramana - J Phys 92, 26 (2019). https://doi.org/10.1007/s12043-018-1684-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-018-1684-0

Keywords

PACS Nos

Search

Navigation