Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Experimental verification of quantum computation


Quantum computers are expected to offer substantial speed-ups over their classical counterparts and to solve problems intractable for classical computers. Beyond such practical significance, the concept of quantum computation opens up fundamental questions, among them the issue of whether quantum computations can be certified by entities that are inherently unable to compute the results themselves. Here we present the first experimental verification of quantum computation. We show, in theory and experiment, how a verifier with minimal quantum resources can test a significantly more powerful quantum computer. The new verification protocol introduced here uses the framework of blind quantum computing and is independent of the experimental quantum-computation platform used. In our scheme, the verifier is required only to generate single qubits and transmit them to the quantum computer. We experimentally demonstrate this protocol using four photonic qubits and show how the verifier can test the computer’s ability to perform quantum computation.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Concept of a quantum prover interactive proof system based on blind quantum computing.
Figure 2: Measurement verification.
Figure 3: Schematic of a quantum computation with verification sub-routines.
Figure 4: A blind Bell test for the verification of quantum resources.


  1. Deutsch, D. Quantum theory, the Church–Turing principle and the universal quantum computer. Proc. R. Soc. A 400, 97–117 (1985).

    ADS  MathSciNet  Article  Google Scholar 

  2. Deutsch, D. & Jozsa, R. Rapid solution of problems by quantum computation. Proc. R. Soc. A 439, 553–558 (1992).

    ADS  MathSciNet  Article  Google Scholar 

  3. Grover, L. K. in Proc. 28th Annual ACM Symp. on the Theory of Computing (ed. Miller, G. L.) 212–219 (ACM, 1996).

    Google Scholar 

  4. Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997).

    MathSciNet  Article  Google Scholar 

  5. Harrow, A. W., Hassidim, A. & Lloyd, S. Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103, 150502 (2009).

    ADS  MathSciNet  Article  Google Scholar 

  6. Feynman, R. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).

    MathSciNet  Article  Google Scholar 

  7. Watrous, J. in Computational Complexity (ed. Meyers, R. A.) 2361–2387 (Springer, 2012).

    Book  Google Scholar 

  8. Pappa, A., Chailloux, A., Wehner, S., Diamanti, E. & Kerenidis, I. Multipartite entanglement verification resistant against dishonest parties. Phys. Rev. Lett. 108, 260502 (2012).

    ADS  Article  Google Scholar 

  9. Aharonov, D., Ben-Or, M. & Eban, E. Proc. Innovations in Computer Science 453 (ICS, 2010).

    Google Scholar 

  10. Broadbent, A., Fitzsimons, J. & Kashefi, E. Proc. 50th Ann. Symp. Found. Comp. Sci. 517–526 (IEEE Computer Society, 2009).

    Google Scholar 

  11. Aharonov, D. & Vazirani, U. V. Computability: Turing, Gödel, Church, and Beyond 329 (MIT Press, 2013).

    Google Scholar 

  12. Fitzsimons, J. & Kashefi, E. Unconditionally verifiable blind computation. Preprint at (2012).

  13. Morimae, T. No-signaling topological quantum computation in intelligent environment. Preprint at (2012).

  14. Reichardt, B., Unger, F. & Vazirani, U. Classical command of quantum systems. Nature 496, 456–460 (2013).

    ADS  Article  Google Scholar 

  15. Babai, L. Proc. 17th Ann. ACM Symp. Theory Comput. 421–429 (ACM, 1985).

    Google Scholar 

  16. Goldwasser, S., Micali, S. & Rackoff, C. The knowledge complexity of interactive proof systems. SIAM J. Comput. 18, 186–208 (1989).

    MathSciNet  Article  Google Scholar 

  17. Morimae, T. & Fujii, K. Blind topological measurement-based quantum computation. Nature Commun. 3, 1036 (2012).

    ADS  Article  Google Scholar 

  18. Barz, S. et al. Demonstration of blind quantum computing. Science 335, 303–308 (2012).

    ADS  MathSciNet  Article  Google Scholar 

  19. Raussendorf, R. & Briegel, H. A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001).

    ADS  Article  Google Scholar 

  20. Raussendorf, R., Browne, D. E. & Briegel, H. J. Measurement-based quantum computation with cluster states. Phys. Rev. A 68, 022312 (2003).

    ADS  Article  Google Scholar 

  21. Bell, J. On the Einstein–Podolsky–Rosen paradox. Physics 1, 195–200 (1964).

    MathSciNet  Article  Google Scholar 

  22. Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969).

    ADS  Article  Google Scholar 

  23. Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001).

    ADS  Article  Google Scholar 

  24. Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).

    ADS  Article  Google Scholar 

  25. Dunjko, V., Kashefi, E. & Leverrier, A. Blind quantum computing with weak coherent pulses. Phys. Rev. Lett. 108, 200502 (2012).

    ADS  Article  Google Scholar 

  26. Morimae, T. & Fujii, K. Blind quantum computation protocol in which Alice only makes measurements. Phys. Rev. A 87, 050301 (2013).

    ADS  Article  Google Scholar 

  27. Weitenberg, C. et al. Single-spin addressing in an atomic Mott insulator. Nature 471, 319–324 (2011).

    ADS  Article  Google Scholar 

  28. Islam, R. et al. Onset of a quantum phase transition with a trapped ion quantum simulator. Nature Commun. 2, 377 (2011).

    ADS  Article  Google Scholar 

  29. Monz, T. et al. 14-qubit entanglement: Creation and coherence. Phys. Rev. Lett. 106, 130506 (2011).

    ADS  Article  Google Scholar 

  30. Britton, J. et al. Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins. Nature 484, 489–492 (2012).

    ADS  Article  Google Scholar 

  31. Leibfried, D. Could a boom in technologies trap Feynman’s simulator? Nature 463, 608–608 (2010).

    ADS  Article  Google Scholar 

  32. Aaronson, S. Proc. 36th Ann. ACM Symp. Theory Comput. 118–127 (ACM, 2004).

    Google Scholar 

Download references


The authors are grateful to S. Aaronson, D. Aharonov, C. Brukner, A. Zeilinger and F. Verstraete for discussions. S.B. and P.W. acknowledge support from the European Commission, Q-ESSENCE (No. 248095), QUILMI (No. 295293), EQUAM (No. 323714), PICQUE (No. 608062) and the ERA-Net CHISTERA project QUASAR, the John Templeton Foundation, the Vienna Center for Quantum Science and Technology (VCQ), the Austrian Nano-initiative NAP Platon, the Austrian Science Fund (FWF) through the SFB FoQuS (No. F4006-N16), START (No. Y585- N20) and the doctoral programme CoQuS, the Vienna Science and Technology Fund (WWTF) under grant ICT12-041, and the Air Force Office of Scientific Research, Air Force Material Command, United States Air Force, under grant number FA8655-11-1-3004. J.F.F. acknowledges support from the National Research Foundation and the Ministry of Education, Singapore. This material is based on research supported in part by the Singapore National Research Foundation under NRF Award No. NRF-NRFF2013-01. E.K. acknowledges support from UK Engineering and Physical Sciences Research Council (EP/E059600/1).

Author information

Authors and Affiliations



S.B. designed and performed the experiments, acquired the experimental data, carried out theoretical calculations and the data analysis, and wrote the manuscript. J.F.F. and E.K. carried out theoretical calculations, contributed the proofs, and wrote the manuscript. P.W. designed the experiment, edited the manuscript and supervised the project.

Corresponding authors

Correspondence to Stefanie Barz or Philip Walther.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 1424 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Barz, S., Fitzsimons, J., Kashefi, E. et al. Experimental verification of quantum computation. Nature Phys 9, 727–731 (2013).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing