Skip to main content
SpringerLink
Log in

A Logic for Formal Verification of Quantum Programs

  • Conference paper
Advances in Computer Science - ASIAN 2009. Information Security and Privacy (ASIAN 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5913))

Included in the following conference series:

Abstract

This paper provides a Hoare-style logic for quantum computation. While the usual Hoare logic helps us to verify classical deterministic programs, our logic supports quantum probabilistic programs. Our target programming language is QPL defined by Selinger, and our logic is an extension of the probabilistic Hoare-style logic defined by den Hartog. In this paper, we demonstrate how the quantum Hoare-style logic proves properties of well-known algorithms.

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

Access this chapter

Log in via an institution
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.

References

  1. Hoare, C.A.R.: An axiomatic basis for computer programming. Communications of ACM 12, 576–580 (1969)

    Article  MATH  Google Scholar 

  2. Cook, S.A.: Soundness and completeness of an axiom system for program verification. SIAM Journal on Computing 7(1), 70–78 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  3. Harel, D., Kozen, D., Tiuryn, J.: Dynamic logic. In: Handbook of Philosophical Logic, pp. 497–604. MIT Press, Cambridge (1984)

    Google Scholar 

  4. Selinger, P.: Towards a quantum programming language. Mathematical Structures in Computer Science 14(4), 527–586 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. den Hartog, J.I.: Verifying probabilistic programs using a Hoare-like logic. In: Thiagarajan, P.S., Yap, R.H.C. (eds.) ASIAN 1999. LNCS, vol. 1742, pp. 113–125. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  6. Bennet, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolski-Rosen channels. Physical Review Letters 70, 1895–1899 (1993)

    Article  MathSciNet  Google Scholar 

  7. Shor, P.W.: Algorithms for quantum computation. In: Foundations of Computer Science, pp. 124–134. IEEE Computer Society Press, Los Alamitos (1994)

    Google Scholar 

  8. Cleve, R., Ekert, A.K., Macchiavello, C., Mosca, M.: Quantum algorithms revised. Proceedings of Royal Society London A 454, 339–354 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  9. Bennet, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Computers, Systems and Signal Processing, pp. 175–179. IEEE Computer Society, Los Alamitos (1984)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  11. Brunet, O., Jorrand, P.: Dynamic quantum logic for quantum programs. International Journal of Quantum Information 2(1) (2004)

    Google Scholar 

  12. Chadha, R., Mateus, P., Sernadas, A.: Reasoning about imperative quantum programs. In: Mathematical Foundations of Programming Semantics. ENTCS, vol. 158, pp. 19–39. Elsevier, Amsterdam (2006)

    Google Scholar 

  13. D’Hondt, E., Panangaden, P.: Quantum weakest preconditions. Mathematical Structures in Computer Science 16(3), 429–451 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. Ying, M.S.: Hoare logic for quantum programs (2009) arXiv:0906.4586v1

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  17. Mayers, D.: Unconditional security in quantum cryptography. Journal of ACM 48(3), 351–406 (2001)

    Article  MathSciNet  Google Scholar 

  18. Feng, Y., Duan, R.Y., Ji, Z.F., Ying, M.S.: Proof rules for the correctness of quantum programs. Theoretical Computer Science 386(1,2), 151–166 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  19. Altenkirch, T., Grattage, J.: A functional quantum programming language. In: Logic in Computer Science, pp. 249–258. IEEE Computer Society, Los Alamitos (2005)

    Google Scholar 

  20. Floyd, R.W.: Assigning meanings to programs. In: Applied Mathematics, AMS, pp. 19–32 (1967)

    Google Scholar 

  21. Bloom, S., Ésik, Z.: Floyd-Hoare logic in iteration theories. Journal of ACM 38(4), 887–934 (1991)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Science, University of Tokyo,  

    Yoshihiko Kakutani

Authors
  1. Yoshihiko Kakutani
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Carnegie Mellon University, 5000 Forbes Ave, 15213, Pittsburgh, PA, USA

    Anupam Datta

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kakutani, Y. (2009). A Logic for Formal Verification of Quantum Programs. In: Datta, A. (eds) Advances in Computer Science - ASIAN 2009. Information Security and Privacy. ASIAN 2009. Lecture Notes in Computer Science, vol 5913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10622-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-10622-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10621-7

  • Online ISBN: 978-3-642-10622-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation