On Certified Randomness from Fourier Sampling or Random Circuit Sampling

Roozbeh Bassirian; Adam Bouland; Bill Fefferman; Sam Gunn; Avishay Tal

doi:10.22331/q-2026-02-10-2002

On Certified Randomness from Fourier Sampling or Random Circuit Sampling

Roozbeh Bassirian¹, Adam Bouland², Bill Fefferman¹, Sam Gunn³, and Avishay Tal³

¹University of Chicago
²Stanford University
³UC Berkeley

Published:	2026-02-10, volume 10, page 2002
Editor:	Alexander Dalzell
Eprint:	arXiv:2111.14846v3
Doi:	https://doi.org/10.22331/q-2026-02-10-2002
Citation:	Quantum 10, 2002 (2026).

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Abstract

Certified randomness has a long history in quantum information, with many potential applications. Recently Aaronson and Hung proposed a novel public certified randomness protocol based on existing random circuit sampling (RCS) experiments. The security of their protocol, however, relies on non-standard complexity-theoretic conjectures which were not previously studied in the literature.

Inspired by this work, we study certified randomness in the quantum random oracle model (QROM). We show that quantum Fourier Sampling can be used to define a publicly verifiable certified randomness protocol with black-box security without any computational assumptions. In addition to giving a certified randomness protocol in the QROM, our work can also be seen as supporting Aaronson and Hung's conjectures for RCS-based randomness generation, as our protocol is in some sense the "black-box version" of Aaronson and Hung's protocol. In further support of Aaronson and Hung's proposal, we prove a Fourier Sampling version of Aaronson and Hung's conjecture by extending Raz and Tal's separation of BQP vs PH.

Our work complements the subsequent certified randomness protocol of Yamakawa and Zhandry (2022) in the QROM. Whereas the security of that protocol relied on the Aaronson-Ambainis conjecture, ours does not rely on any computational assumption – at the expense of requiring exponential-time classical verification. Our protocol also has a simple heuristic implementation.

► BibTeX data

@article{Bassirian2026certifiedrandomness,
  doi = {10.22331/q-2026-02-10-2002},
  url = {https://doi.org/10.22331/q-2026-02-10-2002},
  title = {On {C}ertified {R}andomness from {F}ourier {S}ampling or {R}andom {C}ircuit {S}ampling},
  author = {Bassirian, Roozbeh and Bouland, Adam and Fefferman, Bill and Gunn, Sam and Tal, Avishay},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2002},
  month = feb,
  year = {2026}
}

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