iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://unpaywall.org/10.1007/11783596_25
Quantum Predicative Programming | SpringerLink
Skip to main content
Springer Nature Link
Log in

Quantum Predicative Programming

  • Conference paper
Mathematics of Program Construction (MPC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4014))

Included in the following conference series:

Abstract

The subject of this work is quantum predicative programming — the development of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming methodology. Our work is based on probabilistic predicative programming, a recent generalisation of the well-established predicative programming. It supports the style of program development in which each programming step is proven correct as it is made. We inherit the advantages of the theory, such as its generality, simple treatment of recursive programs, time and space complexity, and communication. Our theory of quantum programming provides tools to write both classical and quantum specifications, develop quantum programs that implement these specifications, and reason about their comparative time and space complexity all in the same framework.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Knill, E.: Conventions for quantum pseudocode. Techn. Report LAUR-96-2724. Los Alamos National Laboratory (1996)

    Google Scholar 

  2. Hehner, E.: A Practical Theory of Programming. Springer, Heidelberg (1993), New edition available free at: http://www.cs.utoronto.ca/~hehner/aPToP/

    MATH  Google Scholar 

  3. Hehner, E.C.R.: Probabilistic predicative programming. In: Kozen, D. (ed.) MPC 2004. LNCS, vol. 3125, pp. 169–185. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  4. Ömer, B.: Quantum programming in QCL. Master’s thesis. TU Vienna (2000)

    Google Scholar 

  5. Bettelli, S., Calarco, T., Serafini, L.: Toward an architecture for quantum programming. European Physical J. D 25(2), 181–200 (2003)

    Article  Google Scholar 

  6. Sanders, J.W., Zuliani, P.: Quantum programming. In: Backhouse, R., Oliveira, J.N. (eds.) MPC 2000. LNCS, vol. 1837, pp. 80–99. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  7. Morgan, C., McIver, A.: pQCL: formal reasoning for random algorithms. South African Computer J. 22, 14–27 (1999)

    Google Scholar 

  8. Zuliani, P.: Non-deterministic quantum programming. In: QPL 2004, pp. 179–195 (2004)

    Google Scholar 

  9. Zuliani, P.: Quantum programming with mixed states. In: QPL 2005 (2005)

    Google Scholar 

  10. Aharonov, D., Kitaev, A., Nisan, N.: Quantum circuits with mixed states. In: Proc. of 30th Ann. ACM Symp. on Theory of Computing, STOC 1998, pp. 20–30. ACM Press, New York (1998)

    Chapter  Google Scholar 

  11. Zuliani, P.: Compiling quantum programs. Acta Inform. 41(7-8), 435–474 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. Butler, M.J., Hartel, P.H.: Reasoning about grover’s quantum search algorithm using probabilistic wp. ACM Trans. on Program. Lang. and Syst. 21(3), 417–429 (1999)

    Article  Google Scholar 

  13. Boyer, M., Brassard, G., Høyer, P., Tapp, A.: Tight bounds on quantum searching. In: Fortschritte der Physik, pp. 493–506 (1998)

    Google Scholar 

  14. Adao, P., Mateus, P.: A process algebra for reasoning about quantum security. In: QPL 2005 (2005)

    Google Scholar 

  15. Lalire, M., Jorrand, P.: A process algebraic approach to concurrent and distributed quantum computation: operational semantics. In: QPL 2004, pp. 109–126 (2004)

    Google Scholar 

  16. Jorrand, P., Lalire, M.: Toward a quantum process algebra. In: Proc. of 1st ACM Conf. on Computing Frontiers, pp. 111–119. ACM Press, New York (2004)

    Chapter  Google Scholar 

  17. Abramsky, S.: High-level methods for quantum computation and information. In: Proc. of 19th Ann. IEEE Symp. on Logic in Computer Science, LICS 2004, pp. 410–414. IEEE Comput. Soc. Press, Los Alamitos (2004)

    Chapter  Google Scholar 

  18. Abramsky, S., Coecke, B.: A categorical semantics of quantum protocols. In: Proc. of 19th Ann. IEEE Symp. on Logic in Computer Science, LICS 2004, pp. 415–425. IEEE Comput. Soc. Press, Los Alamitos (2004)

    Chapter  Google Scholar 

  19. Abramsky, S., Duncan, R.: A categorical quantum logic. In: QPL 2004, pp. 3–20 (2004)

    Google Scholar 

  20. Coecke, B.: The logic of entanglement. quant-ph/0402014 (2004)

    Google Scholar 

  21. Selinger, P.: Towards a quantum programming language. Math. Struct. in Comput. Sci. 14(4), 527–586 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  22. Arrighi, P., Dowek, G.: Operational semantics for formal tensorial calculus. In: QPL 2004, pp. 21–38 (2004)

    Google Scholar 

  23. Arrighi, P., Dowek, G.: Linear-algebraic lambda-calculus. In: QPL 2005 (2005)

    Google Scholar 

  24. Altenkirch, T., Grattage, J.: A functional quantum programming language. In: Proc. of 20th Ann. IEEE Symp. on Logic in Computer Science, LICS 2005, pp. 249–258. IEEE Comput. Soc. Press, Los Alamitos (2005)

    Google Scholar 

  25. Altenkirch, T., Grattage, J., Vizzotto, J.K., Sabry, A.: An algebra of pure quantum programming. In: QPL 2005 (2005)

    Google Scholar 

  26. D’Hondt, E., Panangaden, P.: Quantum weakest precondition. In: QPL 2004, pp. 75–90 (2004)

    Google Scholar 

  27. D’Hondt, E., Panangaden, P.: Reasoning about quantum knowledge. quant-ph/0507176 (2005)

    Google Scholar 

  28. Danos, V., D’Hondt, E., Kashefi, E., Panangaden, P.: Distributed measurement-based quantum computation. In: QPL 2005 (2005)

    Google Scholar 

  29. Gay, S.J., Nagarajan, R.: Communicating quantum processes. In: Proc. of 32nd ACM SIGACT-SIGPLAN Symp. on Principles of Programming Languages, POPL 2005, pp. 145–157. ACM Press, New York (2005)

    Chapter  Google Scholar 

  30. Selinger, P.: Towards a semantics for higher-order quantum computation. In: QPL 2004 (2004)

    Google Scholar 

  31. Valiron, B.: Quantum typing. In: QPL 2004, pp. 163–178 (2004)

    Google Scholar 

  32. van Tonder, A.: A lambda calculus for quantum computation. SIAM J. of Computing 33(5), 1109–1135 (2004)

    Article  MATH  Google Scholar 

  33. Bennet, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. In: Proc. of 1984 IEEE Int. Conf. on Computers, Systems and Signal Processing, pp. 175–179. IEEE, Los Alamitos (1984)

    Google Scholar 

  34. Yimsiriwattana, A., Lomonaco Jr., S.J.: Distributed quantum computing: A distributed Shor algorithm (2004), http://arxiv.org/abs/quant-ph/0403146v1

  35. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  36. Hehner, E.C.R.: Retrospective and prospective for unifying theories of programming. In: Dunne, S., Stoddart, B. (eds.) UTP 2006. LNCS, vol. 4010, pp. 1–17. Springer, Heidelberg (to appear, 2006)

    Chapter  Google Scholar 

  37. Tafliovich, A.: Quantum programming. Master’s thesis, University of Toronto (2004)

    Google Scholar 

  38. Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. of Royal Society of London A 400, 97–117 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  39. Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. Proc. of Royal Society of London A 439, 553–558 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  40. Jozsa, R.: Quantum algorithms and the Fourier transform. Proc. of Royal Society of London A 454, 323–337 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  41. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proc. of 28th Ann. ACM Symp. on Theory of Computing, STOC 1996, pp. 212–219. ACM Press, New York (1996)

    Chapter  Google Scholar 

  42. Ambainis, A.: Quantum search algorithms. SIGACT News 35(2), 22–35 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of Toronto, Toronto, ON M5S 3G4, Canada

    Anya Tafliovich & Eric C. R. Hehner

Authors
  1. Anya Tafliovich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eric C. R. Hehner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, EE-12618, Tallinn, Estonia

    Tarmo Uustalu

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tafliovich, A., Hehner, E.C.R. (2006). Quantum Predicative Programming. In: Uustalu, T. (eds) Mathematics of Program Construction. MPC 2006. Lecture Notes in Computer Science, vol 4014. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11783596_25

Download citation

  • DOI: https://doi.org/10.1007/11783596_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35631-8

  • Online ISBN: 978-3-540-35632-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation