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Interactive cryptographic proofs of quantumness using mid-circuit measurements

Nature Physics volume 19, pages 1725–1731 (2023)Cite this article

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Abstract

The ability to perform measurements in the middle of a quantum circuit is a powerful resource. It underlies a wide range of applications, from remote state preparation to quantum error correction. Here we apply mid-circuit measurements for a particular task: demonstrating quantum computational advantage. The goal of such a demonstration is for a quantum device to perform a computational task that is infeasible for a classical device with comparable resources. In contrast to existing demonstrations, the distinguishing feature of our approach is that the classical verification process is efficient, both in asymptotic complexity and in practice. Furthermore, the classical hardness of performing the task is based upon well-established cryptographic assumptions. Protocols with these features are known as cryptographic proofs of quantumness. Using a trapped-ion quantum computer, we perform mid-circuit measurements by spatially isolating portions of the ion chain via shuttling. This enables us to implement two interactive cryptographic proofs of quantumness, which when suitably scaled to larger systems, promise the efficient verification of quantum computational advantage. Our methods can be applied to a range of interactive quantum protocols.

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Fig. 1: Schematic diagram of an interactive quantum verification protocol.
Fig. 2: Mid-circuit measurements with shuttling.
Fig. 3: Circuit and experimental results.

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Data availability

All data supporting the findings of this study are available in the paper or Methods. The raw experimental data are available from the corresponding author upon reasonable request.

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Acknowledgements

We are grateful to V. Uhlir for the design of the verifier and prover figures. This work is supported by the Army Research Office (ARO) through the LogiQ programme of the Intelligence Advanced Research Projects Activity; the National Quantum Information Science Research Centers, Office of Science, US Department of Energy (DoE); the Quantum Systems Accelerator; the Air Force Office of Scientific Research (AFOSR) Multidisciplinary University Research Initiatives (MURIs) on Quantum Measurement/Verification and Quantum Interactive Protocols (Grant No. FA9550-18-1-0161) and Dissipation Engineering in Open Quantum Systems; the Software-Tailored Architecture for Quantum Co-design Program of the National Science Foundation (NSF); the ARO MURI on Modular Quantum Circuits; the Accelerated Research in Quantum Computing Program, Advanced Scientific Computing Research, DoE (Award No. DE-SC0020312); the Young Investigator Program of the AFOSR (Award No. FA9550-16-1-0495); the Quantum Leap Challenge Institutes, NSF (Grant No. OMA-2016245); the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1125565); the Gordon and Betty Moore Foundation (Grant No. GBMF-12500028); Dr Max Rössler and the Walter Haefner Foundation through the ETH Zürich Foundation; the NSF (Award No. DMR-1747426); a Vannevar Bush Faculty Fellowship; the Office of Advanced Scientific Computing Research under the Accelerated Research in Quantum Computing Program; the A. P. Sloan Foundation; and the David and Lucile Packard Foundation.

Author information

Author notes

  1. These authors contributed equally: Daiwei Zhu, Gregory D. Kahanamoku-Meyer.

Authors and Affiliations

  1. Joint Quantum Institute, and Department of Physics, NIST/University of Maryland, College Park, MD, USA

    Daiwei Zhu, Crystal Noel, Bahaa Harraz, Qingfeng Wang, Andrew Risinger, Lei Feng, Debopriyo Biswas, Laird Egan, Marko Cetina & Christopher Monroe

  2. Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD, USA

    Daiwei Zhu, Qingfeng Wang, Andrew Risinger, Lei Feng, Debopriyo Biswas, Laird Egan & Christopher Monroe

  3. Departments of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA

    Daiwei Zhu, Andrew Risinger & Christopher Monroe

  4. IonQ, Inc., College Park, MD, USA

    Daiwei Zhu

  5. Department of Physics, University of California, Berkeley, CA, USA

    Gregory D. Kahanamoku-Meyer, Umesh Vazirani & Norman Y. Yao

  6. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Gregory D. Kahanamoku-Meyer, Umesh Vazirani & Norman Y. Yao

  7. Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA

    Laura Lewis, Alexandru Gheorghiu & Thomas Vidick

  8. Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA, USA

    Laura Lewis

  9. Duke Quantum Center and Department of Physics, Duke University, Durham, NC, USA

    Crystal Noel, Or Katz, Bahaa Harraz, Marko Cetina & Christopher Monroe

  10. Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA

    Crystal Noel, Or Katz, Bahaa Harraz, Marko Cetina & Christopher Monroe

  11. Chemical Physics Program and Institute for Physical Science and Technology, University of Maryland, College Park, MD, USA

    Qingfeng Wang

  12. Institute for Theoretical Studies, ETH Zürich, Zürich, Switzerland

    Alexandru Gheorghiu

  13. Department of Physics, University of Maryland, College Park, MD, USA

    Yunseong Nam

  14. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel

    Thomas Vidick

  15. Department of Physics, Harvard University, Cambridge, MA, USA

    Norman Y. Yao

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Contributions

D.Z., G.K.M., L.L., C.N., A.G., T.V., U.V., N.Y., M.C. and C.M. designed the research. D.Z., C.N., O.K., B.H., Q.W., A.R., L.F., D.B. and L.E. performed the experiments and collected the data. D.Z., G.K.M., L.L., C.N., L.E., A.G. and Y.N. compiled and optimized the circuit. D.Z., G.K.M. and L.L. analysed the data. All authors contributed to the preperation of the paper.

Corresponding author

Correspondence to Daiwei Zhu.

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Competing interests

C.M. is the chief scientist for IonQ, Inc. and has a personal financial interest in the company. The other authors declare no competing interests.

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Nature Physics thanks Robin Blume-Kohout and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

The supplementary information includes these sections: Result data, Post-selection, Circuit construction of the factoring-based protocol, Circuit construction of the LWE-based protocol, Instances of LWE implemented and Additional instances of factoring-based protocols.

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Zhu, D., Kahanamoku-Meyer, G.D., Lewis, L. et al. Interactive cryptographic proofs of quantumness using mid-circuit measurements. Nat. Phys. 19, 1725–1731 (2023). https://doi.org/10.1038/s41567-023-02162-9

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