Skip to main content

Analysis of Classical and Quantum Computing Based on Grover and Shor Algorithm

  • Conference paper
  • First Online:

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 78))

Abstract

Quantum Computing is the study of evolving computing technology. It works with qubits (quantum bits), unlike classical computing (which works on classical bits). A quantum computer can do multiple tasks at a time and that’s why they are more efficient than traditional computers. In this paper, it has been thoroughly discussed about qubits, Superposition of qubits, gates, Superdense Coding, quantum programming languages and specially algorithms and how they are better than the best known classical algorithms. There is an exponential speedup in many of the operations performed by quantum algorithms as compared to classical algorithms. They are compared on their complexities. Most highly recognized algorithms in the field of quantum computing are: Grover’s algorithm for database search and Shor’s algorithm for factoring large integers into two prime numbers efficiently. In future, if quantum computers are made, it would be easier to encrypt the information that should not be revealed such as government databases in a new and secure way. Here, we will discuss about the commands used in quantum computing language (QCL) and mathematical proofs of few of the algorithms such as Deutsch–Jozsa algorithm, etc.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. E. Aïmeur, G. Brassard, S. Gambs, Machine learning in a quantum world, in: L. Lamontagne, M. Marchand (Eds.), Proceedings of Canadian AI 2006, in: LNAI, vol. 4013, Springer, 2006, pp. 431–442.

    Google Scholar 

  2. S.L. Andresen, John McCarthy: Father of AI, IEEE Intelligent Systems (September/October 2002) 84–85.

    Google Scholar 

  3. A. Baltag, S. Smets, LQP: The dynamic logic of quantum information, Mathematical Structures in Computer Science 16 (2006) 491–525.

    Google Scholar 

  4. A. Barenco, C. Bennet, R. Cleve, D.P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J.A. Smolin, H. Weinfurter, Elementary gates for quantum computation, Physical Review A 52 (1995) 3457–3467.

    Google Scholar 

  5. P.A. Benioff, The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines, Journal of Statistical Physics 22 (1980) 563–591.

    Google Scholar 

  6. S.C. Benjamin, P.M. Hayden, Multiplayer quantum games, Physical Review A 64 (2001), art. no. 030301.

    Google Scholar 

  7. S. Bettelli, T. Calarco, L. Serafini, Toward an architecture for quantum programming, The European Physical Journal D 25 (2003) 181–200.

    Google Scholar 

  8. G. Cattaneo, M.L. Dalla Chiara, R. Giuntini, R. Leporini, An unsharp logic from quantum computation, International Journal of Theoretical Physics 43 (2004) 1803–1817.

    Google Scholar 

  9. R.Y. Duan, Y. Feng, M.S. Ying, Entanglement is not necessary for perfect discrimination between unitary operations, Physical Review Letters 98 (2007), art. no. 100503.

    Google Scholar 

  10. E. Bernstein, U. Vazirani, Quantum complexity theory, SIAM Journal on Computing 26 (1997) 1411–1473.

    Google Scholar 

  11. Wilde, Mark (18 April 2013). Quantum Information Theory. Cambridge University Press. p. 181. ISBN 978-1-107-03425-9.

    Google Scholar 

  12. Nielsen, Michael A.; Chuang, Isaac L. (9 December 2010). “2.3 Application: superdense coding”. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press. p. 97. ISBN 978-1-139-49548-6.

    Google Scholar 

  13. A. Bertoni, C. Mereghetti, B. Palano, Quantum computing: 1-way quantum automata, in: Z. Esik, Z. Fulop (Eds.), Proceedings of 7th International Conference on Developments in Language Theory, in: LNCS, vol. 2710, Springer, 2003, pp. 1–20.

    Google Scholar 

  14. G. Birkhoff, J. von Neumann, The logic of quantum mechanics, Annals of Mathematics 37 (1936) 823–843.

    Google Scholar 

  15. R. Bonner, R. Freivalds, A survey of quantum learning, in: R. Bonner, R. Freivalds (Eds.), Proceedings of the 3rd Workshop on Quantum Computation and Learning, 2002, pp. 106–119.

    Google Scholar 

  16. T. Altenkirch, J. Grattage, A functional quantum programming language, in: Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science (LICS), 2005, pp. 249–258 Dr Iain Styles], “The Quantum Fourier transform” .

    Google Scholar 

  17. O. Brunet, P. Jorrand, Dynamic quantum logic for quantum programs, International Journal of Quantum Information 2 (2004) 45–54.

    Google Scholar 

  18. R. Chadha, P. Mateus, A. Sernadas, Reasoning about imperative quantum programs, Electronic Notes in Theoretical Computer Science 158 (2006) 19–39.

    Google Scholar 

  19. T. F. Havel, C. J. L. Doran, “A Bloch-Sphere-Type Model for Two Qubits in the Geometric Algebra of a 6-D Euclidean Vector Space”, PROC. SPIE THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING Vol.5436, 93-106 (2004), 2nd Conf. Quantum information and computation; arXiv:quantph/0403136

  20. Bennett, C.; Wiesner, S. (1992). “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states”. Physical Review Letters. 69 (20): 2881. PMID 10046665. doi:10.1103/PhysRevLett.69.2881

  21. Julian Brown, “Minds, Machines and Multiverse: The Quest for the Quantum Computer”

    Google Scholar 

  22. P. Shor, ‘Quantum computing’, proceedings of the International Congress of Mathematicians, 1998.

    Google Scholar 

  23. Stephane Beauregard, “Circuit for Shor’s algorithm using 2n+3 qubits”, Quantum Information and Computation, Vol. 3, No. 2 (2003) pp. 175–185.

    Google Scholar 

  24. P. Bruza, K. Kitto, D. Nelson, C. McEvoy, Extracting spooky-activation-at-a-distance from considerations of entanglement, in: P. Bruza, et al. (Eds.), Proceedings of Third International Symposium on Quantum Interaction, in: LNCS, vol. 5494, Springer-Verlag, 2009, pp. 71–83.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gaurav Raj .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Raj, G., Singh, D., Madaan, A. (2018). Analysis of Classical and Quantum Computing Based on Grover and Shor Algorithm. In: Satapathy, S., Bhateja, V., Das, S. (eds) Smart Computing and Informatics . Smart Innovation, Systems and Technologies, vol 78. Springer, Singapore. https://doi.org/10.1007/978-981-10-5547-8_43

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-5547-8_43

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-5546-1

  • Online ISBN: 978-981-10-5547-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics