Skip to main content

Potential Applications

  • Chapter
  • First Online:
  • 1768 Accesses

Part of the book series: Quantum Science and Technology ((QST))

Abstract

As some problems are best solved in classical computation with algorithms based on random walks, it is expected that this type of problems could be solved even faster using quantum walks (Knight et al. 2003b). Kendon (2006b) gave an introductory overview of quantum walk algorithms in the context of prospects for practical quantum computing, particularly in three areas: (a) simulation of classical systems; (b) simulation of quantum systems; and (c) analogue computing. Another review of the subject is provided by Ambainis (2003) who highlighted two main classes of quantum walk algorithms (a) exponentially faster hitting and (b) quantum walk based search. In this chapter we will examine these and a number of other algorithmic applications of quantum walks.

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   109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   139.99
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

Bibliography

  • Agliari, E., Blumen, A., Mülken, O.: Phys. Rev. A 82, 012305 (2010)

    Article  ADS  Google Scholar 

  • Ambainis, A.: Int. J. Quantum Inf. 1, 507 (2003)

    Article  MATH  Google Scholar 

  • Ambainis, A.: FOCS04: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 22–31. IEEE Computer Society (2004). arXiv:quant-ph/0311001

    Google Scholar 

  • Ambainis, A., Kempe, J., Rivosh, A.: SODA’05: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1099–1108. Society for Industrial and Applied Mathematics (2005). arXiv:quant-ph/0402107

    Google Scholar 

  • Babai, L., Kantor, W.M., Luks, E.M.: Proceedings of the 24th Annual Symposium on Foundations of Computer Science SFCS ’83, pp. 162–171. IEEE Computer Society (1983)

    Google Scholar 

  • Berry, S.D., Wang, J.B.: Phys. Rev. A 83, 042317 (2011)

    Article  ADS  Google Scholar 

  • Bracken, A.J., Ellinas, D., Smyrnakis, I.: Phys. Rev. A 75, 022322 (2007)

    Article  ADS  Google Scholar 

  • Cai, J.-Y., Fürer, M., Immerman, N.: Combinatorica 12, 389 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  • Carneiro, I., Loo, M., Xu, X., Girerd, M., Kendon, V., Knight, P.L.: New J. Phys. 7, 156 (2005)

    Article  ADS  Google Scholar 

  • Childs, A.M.: Phys. Rev. Lett. 102, 180501 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  • Childs, A., Goldstone, J.: Phys. Rev. A 70, 042312 (2004a)

    Article  MathSciNet  ADS  Google Scholar 

  • Childs, A., Goldstone, J.: Phys. Rev. A 70, 022314 (2004b)

    Article  MathSciNet  ADS  Google Scholar 

  • Childs, A., Farhi, E., Gutmann., S.: Quantum Inf. Process. 1, 35 (2002)

    Google Scholar 

  • Childs, A., Cleve, R., Deotto, E., Farhi, E., Gutmann, S., Spielman, D.: STOC’03: Proceedings of the 35th Annual ACM Symposium on Theory of Computing, pp. 59–68 ACM (2003). arXiv:quant-ph/0209131

    Google Scholar 

  • Douglas, B.L.: (2011). arXiv:1101.5211 and private communication

    Google Scholar 

  • Douglas, B.L., Wang, J.B.: J. Phys. A 41, 075303 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  • Emms, D., Hancock, E.R., Severini, S., Wilson, R.: Electron. J. Comb. 13, R34 (2006)

    MathSciNet  Google Scholar 

  • Farhi, E., Gutmann, S.: Phys. Rev. A 58, 915 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  • Feynman, R.P.: Opt. News 11, 11 (1985)

    Article  Google Scholar 

  • Gamble, J.K., Friesen, M., Zhou, D., Joynt, R., Coppersmith, S.N.:, Phys. Rev. A 81, 052313 (2010)

    Article  ADS  Google Scholar 

  • Gerhardt, H., Watrous, J.: RANDOM’03: Proceedings of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science, Princeton. Lecture Notes in Computer Science, vol. 2764, pp. 290–301. Springer, Berlin/New York (2003)

    Google Scholar 

  • Godsil, C., Royle, G.F.: Algebraic Graph Theory. Graduate Texts in Mathematics, vol. 207. Springer, New York (2001)

    Google Scholar 

  • Grover, L.K.: STOC’96: Proceedings of the 28th Annual ACM Symposium on Theory of Computing, Philadephia, pp. 212–219. ACM, New York (1996)

    Google Scholar 

  • He, P.R., Zhang, W.J., Li, Q.: J. Frankl. Inst. 342, 657 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Kempe, J.: RANDOM’03: Proceedings of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science. Lecture Notes in Computer Science, vol. 2764, pp. 354–369. Springer (2003a). arXiv:quant-ph/0205083

    Google Scholar 

  • Kempe, J.: Contemp. Phys. 44, 307 (2003b)

    Article  ADS  Google Scholar 

  • Kendon, V.M.: Philos. Trans. R. Soc. A 364, 3407 (2006b)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Knight, P.L., Roldán, E., Sipe, J.E.: Phys. Rev. A 68, 020301 (2003b)

    Article  ADS  Google Scholar 

  • Köbler, J.: IN, pp. 241–256. Springer (2006)

    Google Scholar 

  • Moore, C., Russell, A.: RANDOM’02: Proceedings of the 6th International Workshop Randomization and Approximation in Computer Science. Lecture Notes in Computer Science, vol. 2483, pp. 164–178. Springer (2002). arXiv:quant-ph/0104137

    Google Scholar 

  • Reitzner, D., Hillery, M., Feldman, E., Bužek, V.: (2009). arXiv:quant-ph/0805.1237v3

    Google Scholar 

  • Richter, P.C.: New J. Phys. 9, 72 (2007a)

    Article  ADS  Google Scholar 

  • Richter, P.C.: Phys. Rev. A 76, 042306 (2007b)

    Article  ADS  Google Scholar 

  • Shenvi, N., Kempe, J., Whaley, K.B.: Phys. Rev. A 67, 052307 (2003)

    Article  ADS  Google Scholar 

  • Shiau, S.Y., Joynt, R., Coppersmith, S.N.: Quantum Inf. Comput. 5, 492 (2005)

    MathSciNet  MATH  Google Scholar 

  • Strauch, F.W.: Phys. Rev. A 73, 054302 (2006b)

    Article  MathSciNet  ADS  Google Scholar 

  • Tregenna, B., Flanagan, W., Maile, R., Kendon, V.: New J. Phys. 5, 83 (2003)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Manouchehri, K., Wang, J. (2014). Potential Applications. In: Physical Implementation of Quantum Walks. Quantum Science and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36014-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-36014-5_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36013-8

  • Online ISBN: 978-3-642-36014-5

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics