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
Open Access articles citing this article.
Light: Science & Applications Open Access 18 August 2021
Theory of Computing Systems Open Access 06 July 2018
npj Quantum Information Open Access 13 April 2017
Subscribe to Journal
Get full journal access for 1 year
only $8.25 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Deutsch, D. Quantum theory, the Church–Turing principle and the universal quantum computer. Proc. R. Soc. A 400, 97–117 (1985).
Deutsch, D. & Jozsa, R. Rapid solution of problems by quantum computation. Proc. R. Soc. A 439, 553–558 (1992).
Grover, L. K. in Proc. 28th Annual ACM Symp. on the Theory of Computing (ed. Miller, G. L.) 212–219 (ACM, 1996).
Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997).
Harrow, A. W., Hassidim, A. & Lloyd, S. Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103, 150502 (2009).
Feynman, R. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).
Watrous, J. in Computational Complexity (ed. Meyers, R. A.) 2361–2387 (Springer, 2012).
Pappa, A., Chailloux, A., Wehner, S., Diamanti, E. & Kerenidis, I. Multipartite entanglement verification resistant against dishonest parties. Phys. Rev. Lett. 108, 260502 (2012).
Aharonov, D., Ben-Or, M. & Eban, E. Proc. Innovations in Computer Science 453 (ICS, 2010).
Broadbent, A., Fitzsimons, J. & Kashefi, E. Proc. 50th Ann. Symp. Found. Comp. Sci. 517–526 (IEEE Computer Society, 2009).
Aharonov, D. & Vazirani, U. V. Computability: Turing, Gödel, Church, and Beyond 329 (MIT Press, 2013).
Fitzsimons, J. & Kashefi, E. Unconditionally verifiable blind computation. Preprint at http://arxiv.org/abs/1203.5217 (2012).
Morimae, T. No-signaling topological quantum computation in intelligent environment. Preprint at http://arxiv.org/abs/1208.1495 (2012).
Reichardt, B., Unger, F. & Vazirani, U. Classical command of quantum systems. Nature 496, 456–460 (2013).
Babai, L. Proc. 17th Ann. ACM Symp. Theory Comput. 421–429 (ACM, 1985).
Goldwasser, S., Micali, S. & Rackoff, C. The knowledge complexity of interactive proof systems. SIAM J. Comput. 18, 186–208 (1989).
Morimae, T. & Fujii, K. Blind topological measurement-based quantum computation. Nature Commun. 3, 1036 (2012).
Barz, S. et al. Demonstration of blind quantum computing. Science 335, 303–308 (2012).
Raussendorf, R. & Briegel, H. A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001).
Raussendorf, R., Browne, D. E. & Briegel, H. J. Measurement-based quantum computation with cluster states. Phys. Rev. A 68, 022312 (2003).
Bell, J. On the Einstein–Podolsky–Rosen paradox. Physics 1, 195–200 (1964).
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).
Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001).
Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).
Dunjko, V., Kashefi, E. & Leverrier, A. Blind quantum computing with weak coherent pulses. Phys. Rev. Lett. 108, 200502 (2012).
Morimae, T. & Fujii, K. Blind quantum computation protocol in which Alice only makes measurements. Phys. Rev. A 87, 050301 (2013).
Weitenberg, C. et al. Single-spin addressing in an atomic Mott insulator. Nature 471, 319–324 (2011).
Islam, R. et al. Onset of a quantum phase transition with a trapped ion quantum simulator. Nature Commun. 2, 377 (2011).
Monz, T. et al. 14-qubit entanglement: Creation and coherence. Phys. Rev. Lett. 106, 130506 (2011).
Britton, J. et al. Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins. Nature 484, 489–492 (2012).
Leibfried, D. Could a boom in technologies trap Feynman’s simulator? Nature 463, 608–608 (2010).
Aaronson, S. Proc. 36th Ann. ACM Symp. Theory Comput. 118–127 (ACM, 2004).
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).
The authors declare no competing financial interests.
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). https://doi.org/10.1038/nphys2763
This article is cited by
Quantum Information Processing (2022)
Light: Science & Applications (2021)
Quantum Information Processing (2020)
Theory of Computing Systems (2019)
Nature Photonics (2018)