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The Hardness of Learning Quantum Circuits and Its Cryptographic Applications

Authors Bill Fefferman , Soumik Ghosh, Makrand Sinha, Henry Yuen

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Subject Classification

ACM Subject Classification
  • Security and privacy → Cryptography
  • Theory of computation → Quantum complexity theory
Keywords
  • quantum learning
  • quantum circuits
  • cryptographic hardness
  • one-way state generators

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Abstract

We show that concrete hardness assumptions about learning or cloning the output state of a random quantum circuit can be used as the foundation for secure quantum cryptography. In particular, under these assumptions we construct secure one-way state generators (OWSGs), digital signature schemes, quantum bit commitments, and private key encryption schemes. We also discuss evidence for these hardness assumptions by analyzing the best-known quantum learning algorithms, as well as proving black-box lower bounds for cloning and learning given state preparation oracles.
Our random circuit-based constructions provide concrete instantiations of quantum cryptographic primitives whose security do not depend on the existence of one-way functions. The use of random circuits in our constructions also opens the door to {NISQ-friendly quantum cryptography}. We discuss noise tolerant versions of our OWSG and digital signature constructions which can potentially be implementable on noisy quantum computers connected by a quantum network. On the other hand, they are still secure against {noiseless} quantum adversaries, raising the intriguing possibility of a useful implementation of an end-to-end cryptographic protocol on near-term quantum computers. Finally, our explorations suggest that the rich interconnections between learning theory and cryptography in classical theoretical computer science also extend to the quantum setting.

Cite As Get BibTex

Bill Fefferman, Soumik Ghosh, Makrand Sinha, and Henry Yuen. The Hardness of Learning Quantum Circuits and Its Cryptographic Applications. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 56:1-56:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.56

Author Details

Bill Fefferman
  • University of Chicago, IL, USA
Soumik Ghosh
  • University of Chicago, IL, USA
Makrand Sinha
  • University of Illinois Urbana-Champaign, IL, USA
Henry Yuen
  • Columbia University, New York, NY, USA

Funding

B.F. and S.G. acknowledge support from AFOSR (FA9550-21-1-0008). This material is based upon work partially supported by the National Science Foundation under Grant CCF-2044923 (CAREER), by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers (Q-NEXT) and by the DOE QuantISED grant DE-SC0020360. H.Y. acknowledges support from AFOSR award FA9550-23-1-0363, NSF CAREER award CCF-2144219, NSF award CCF-2329939, and the Sloan Foundation. M.S. acknowledges support from the NSF award QCIS-FF: Quantum Computing & Information Science Faculty Fellow at the University of Illinois Urbana-Champaign (NSF 1955032). This work was done in part while some of the authors were visiting the Simons Institute for the Theory of Computing, supported by NSF QLCI Grant No. 2016245.

Acknowledgements

We thank John Bostanci, Jonas Helsen, Yihui Quek, and Abhinav Deshpande for helpful discussions.

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