Experimental verification of quantum computation

Journal name:
Nature Physics
Year published:
Published online


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.

At a glance


  1. Concept of a quantum prover interactive proof system based on blind quantum computing.
    Figure 1: Concept of a quantum prover interactive proof system based on blind quantum computing.

    The verifier wants to find out whether the prover can indeed perform quantum computations. Although the question of whether a classical verifier can test a quantum system is still open, it was shown that a verifier who has access to certain quantum resources can verify quantum computations. Here, in the framework of blind quantum computing, the verifier has to be able to generate single qubits and to transmit them to the prover. After the transmission of the qubits, the verifier and the prover exchange two-way classical communication.

  2. Measurement verification.
    Figure 2: Measurement verification.

    a,b, A blind linear cluster state (a) and a blind rotated horseshoe cluster state (b) that can be used for the preparation of trap qubits. c, Experimental results of the measurement verification. We prepare two different trap states, shown in the figure and in equations (1)– (5), on each qubit 1–4 (for details about the measurements see Supplementary Information) and show the probability of obtaining the correct outcome when measuring those qubits in a basis for which the expected state is an eigenstate.

  3. Schematic of a quantum computation with verification sub-routines.
    Figure 3: Schematic of a quantum computation with verification sub-routines.

    We consider multiple runs of the protocol, where the verifier randomly chooses to run an actual computation or a verification test. The result of the verification test then allows us to conclude whether the computation was performed correctly.

  4. A blind Bell test for the verification of quantum resources.
    Figure 4: A blind Bell test for the verification of quantum resources.

    a, Conventional scheme for a Bell test, where first an (entangled) state is created and then Bell measurements are performed. b,c, The blind zigzag cluster state (b) and its corresponding circuit (c). If the rotation Rz in the lower wire, −δ4+θ4, is chosen equal to zero (or π), the input state in the lower wire will be equal to |0right fenceb (|1right fenceb); otherwise, if the rotation is chosen equal to ±π/2, the input will be |±iright fenceb. The edge between qubits 2 and 3 performs a CPhase gate on the two qubits, which results in an unentangled state in the former case, and in an entangled state in the latter. The values of δ1, δ2 and δ3, as well as the phases θ1, θ2 and θ3, determine the Bell measurement settings shown in equation (6).


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Author information


  1. University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Vienna, Austria

    • Stefanie Barz &
    • Philip Walther
  2. Singapore University of Technology and Design, 20 Dover Drive, Singapore 138682, Singapore

    • Joseph F. Fitzsimons
  3. Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, Singapore 117543, Singapore

    • Joseph F. Fitzsimons
  4. School of Informatics, University of Edinburgh, 10 Crichton Street, Edinburgh EH8 9AB, UK

    • Elham Kashefi


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.

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The authors declare no competing financial interests.

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