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Classical multiparty computation using quantum resources

Marco Clementi, Anna Pappa, Andreas Eckstein, Ian A. Walmsley, Elham Kashefi, and Stefanie Barz
Phys. Rev. A 96, 062317 – Published 18 December 2017
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  • INTRODUCTION
  • THEORY
  • EXPERIMENT AND RESULTS
  • CONCLUSION
  • ACKNOWLEDGMENTS
    • References

    Abstract

    In this work, we demonstrate a way to perform classical multiparty computing among parties with limited computational resources. Our method harnesses quantum resources to increase the computational power of the individual parties. We show how a set of clients restricted to linear classical processing are able to jointly compute a nonlinear multivariable function that lies beyond their individual capabilities. The clients are only allowed to perform classical xor gates and single-qubit gates on quantum states. We also examine the type of security that can be achieved in this limited setting. Finally, we provide a proof-of-concept implementation using photonic qubits that allows four clients to compute a specific example of a multiparty function, the pairwise and.

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    • Received 23 June 2017

    DOI:https://doi.org/10.1103/PhysRevA.96.062317

    ©2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Quantum computationQuantum networks
    Quantum Information, Science & Technology

    Authors & Affiliations

    Marco Clementi1,2, Anna Pappa3,4, Andreas Eckstein1, Ian A. Walmsley1, Elham Kashefi3,5, and Stefanie Barz1,6

    • 1Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
    • 2Department of Physics, University of Pavia, Pavia 27100, Italy
    • 3School of Informatics, University of Edinburgh, Edinburgh EH8 9AB, United Kingdom
    • 4Department of Physics & Astronomy, University College London, London WC1E 6BT, United Kingdom
    • 5LIP6 - CNRS, Université Pierre Et Marie Curie, Paris 75005, France
    • 6Institute for Functional Matter and Quantum Technologies and Center for Integrated Quantum Science and Technology IQST, University of Stuttgart, Stuttgart 70174, Germany

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    Issue

    Vol. 96, Iss. 6 — December 2017

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    • Figure 1
      Figure 1

      A sketch of our scheme for multiparty computation, where a server computes a Boolean function f(x1,x2,...,xn) with inputs xi from different clients. The server generates simple computational resources, such as single qubits, and sends them consecutively to a number of different clients. Each client manipulates the computational resources by performing single-qubit gates. At the end, the server measures the output state. The result of this measurement is sent to the clients, who can deduce the result of the computation.

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    • Figure 2
      Figure 2

      Protocol for delegated multiparty computation. For a description of the protocol, see the main text.

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    • Figure 3
      Figure 3

      Experimental scheme. The server generates heralded, horizontally polarized photons, which are sent to the clients' side. Each client uses a pair of half-wave plates for applying the gates Vri and Uxi. If xi or ri are equal to zero, the setting of the respective half-wave plate is chosen to be zero. If xi or ri are equal to one, the corresponding half-wave plate is rotated by an angle θ with respect to the horizontal polarization state, where θ is given in the figure. Finally, one of the clients performs a final conditional rotation dependent on ⊕ixi. The photon is sent back to the server, where a measurement in the computational basis is performed; this has been implemented using a Wollaston prism and two single-photon Avalanche photodiodes (APDs).

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    • Figure 4
      Figure 4

      (a) Measured outcomes of the computation after decoding r⊕(r⊕f) for a sample subset (x1,x2,x3,x4) of the input bits tested (horizontal axis). (b) Measured outcomes of the computation before decoding (r⊕f), averaged over all possible combinations of ri, i=1,...,4. For each data point, we integrated over 15 s, yielding an overall statistics of about 3000 counts for each computation performed. (c) Long-term stability of our experiment. The graph shows the probability of obtaining the correct outcome measured over 13 h of data acquirement. Every point of the plot corresponds to the average over 1 h of measurement time. The combination of the clients' input bits used here is (x1,x2,x3,x4) = (1,1,1,1).

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