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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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.
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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.
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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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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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DOI: https://doi.org/10.1038/s41567-023-02162-9