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Single-Round Proofs of Quantumness from Knowledge Assumptions

Authors Petia Arabadjieva , Alexandru Gheorghiu , Victor Gitton, Tony Metger

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  • Theory of computation → Cryptographic protocols
Keywords
  • Proofs of quantumness
  • Knowledge assumptions
  • Learning with errors
  • Decisional Diffie-Hellman

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Abstract

A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the certification of quantum devices. Existing single-round protocols based solely on a cryptographic hardness assumption (like asking the quantum computer to factor a large number) require large quantum circuits, whereas multi-round ones use smaller circuits but require experimentally challenging mid-circuit measurements. 
In this work, we construct efficient single-round proofs of quantumness based on existing knowledge assumptions. While knowledge assumptions have not been previously considered in this context, we show that they provide a natural basis for separating classical and quantum computation. Our work also helps in understanding the interplay between black-box/white-box reductions and cryptographic assumptions in the design of proofs of quantumness. Specifically, we show that multi-round protocols based on Decisional Diffie-Hellman (DDH) or Learning With Errors (LWE) can be "compiled" into single-round protocols using a knowledge-of-exponent assumption [Bitansky et al., 2012] or knowledge-of-lattice-point assumption [Loftus et al., 2012], respectively. We also prove an adaptive hardcore-bit statement for a family of claw-free functions based on DDH, which might be of independent interest.

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Petia Arabadjieva, Alexandru Gheorghiu, Victor Gitton, and Tony Metger. Single-Round Proofs of Quantumness from Knowledge Assumptions. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.8

Author Details

Petia Arabadjieva
  • Institute for Theoretical Physics, ETH Zurich, Switzerland
Alexandru Gheorghiu
  • Department of Computer Science and Engineering, Chalmers University of Technology, Göteborg, Sweden
Victor Gitton
  • Institute for Theoretical Physics, ETH Zurich, Switzerland
Tony Metger
  • Institute for Theoretical Physics, ETH Zurich, Switzerland

Funding

P.A., V.G. and T.M. acknowledge support from the ETH Zurich Quantum Center and the Air Force Office for Scientific Research, grant No. FA9550-19-1-0202.
  • Gheorghiu, Alexandru: Knut and Alice Wallenberg Foundation, through the Wallenberg Centre for Quantum Technology (WACQT).
  • Metger, Tony: ETH Doc.Mobility Fellowship.

Acknowledgements

We thank Alex Lombardi, Urmila Mahadev, Greg Kahanamoku-Meyer, Umesh Vazirani, John Wright, and Tina Zhang for helpful discussions. We are especially grateful to Vinod Vaikuntanathan to suggesting many of these ideas in the early stages of the project.

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