Self-testing of Quantum Circuits

  • Frédéric Magniez
  • Dominic Mayers
  • Michele Mosca
  • Harold Ollivier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)

Abstract

We prove that a quantum circuit together with measurement apparatuses and EPR sources can be self-tested, i.e. fully verified without any reference to some trusted set of quantum devices.

To achieve our goal we define the notions of simulation and equivalence. Using these two concepts, we construct sets of simulation conditions which imply that the physical device of interest is equivalent to the one it is supposed to implement. Another benefit of our formalism is that our statements can be proved to be robust.

Finally, we design a test for quantum circuits whose complexity is polynomial in the number of gates and qubits, and the required precision.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Blum, M., Kannan, S.: Designing programs that check their work. J. ACM 42(1), 269–291 (1995)MATHCrossRefGoogle Scholar
  2. 2.
    Blum, M., Luby, M., Rubinfeld, R.: Self-testing/correcting with applications to numerical problems. J. Computer and System Sciences 47(3), 549–595 (1993)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Mayers, D., Yao, A.: Quantum cryptography with imperfect apparatus. In: Proceedings of 39th IEEE FOCS, pp. 503–509 (1998)Google Scholar
  4. 4.
    Dam, W., Magniez, F., Mosca, M., Santha, M.: Self-testing of universal and fault-tolerant sets of quantum gates. In: Proc. of 32nd ACM STOC, pp. 688–696 (2000)Google Scholar
  5. 5.
    Buhrman, H., Fortnow, L., Newman, I., Röhrig, H.: Quantum property testing. In: Proc. of 14th ACM-SIAM SODA, pp. 480–488 (2003)Google Scholar
  6. 6.
    Friedl, K., Magniez, F., Santha, M., Sen, P.: Quantum testers for hidden group properties. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 419–428. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Rudolph, T., Grover, L.: A 2–rebit gate universal for quantum computing (2002)Google Scholar
  8. 8.
    Rubinfeld, R., Sudan, M.: Robust characterizations of polynomials with applications to program testing. SIAM J. Computing 25(2), 23–32 (1996)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Rubinfeld, R.: On the robustness of functional equations. SIAM J. Computing 28, 1972–1997 (1999)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Frédéric Magniez
    • 1
  • Dominic Mayers
    • 2
  • Michele Mosca
    • 3
    • 4
  • Harold Ollivier
    • 4
  1. 1.CNRS–LRIUniversity Paris-SudFrance
  2. 2.Institute for Quantum Information, CaltechUSA
  3. 3.Institute for Quantum ComputingUniversity of WaterlooCanada
  4. 4.Perimeter Institute for Theoretical PhysicsWaterlooCanada

Personalised recommendations