On Certified Randomness from Fourier Sampling or Random Circuit Sampling
arxiv(2021)
摘要
Certified randomness has a long history in quantum information, with many
potential applications. Recently Aaronson (2018, 2020) proposed a novel public
certified randomness protocol based on existing random circuit sampling (RCS)
experiments. The security of his protocol, however, relies on non-standard
complexity-theoretic conjectures which were not previously studied in the
literature.
Inspired by Aaronson's 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
unconditional black-box security. In addition to giving a certified randomness
protocol in the QROM, our work can also be seen as supporting Aaronson's
conjectures for RCS-based randomness generation, as our protocol is in some
sense the "black-box version" of Aaronson's protocol. In further support of
Aaronson's proposal, we prove a Fourier Sampling version of Aaronson'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, our protocol is unconditionally secure - at
the expense of requiring exponential-time classical verification. Our protocol
also has a simple heuristic implementation.
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