On Certified Randomness from Quantum Advantage Experiments.
Roozbeh Bassirian, Adam Bouland, Bill Fefferman, Sam Gunn, Avishay Tal · arXiv (Cornell University) · 2021
Certified randomness has a long history in quantum information, with many potential applications. Recently Aaronson (Aaronson 2018, 2020) proposed a novel certified randomness protocol based on existing random circuit sampling (RCS) experiments -- placing this application within the reach of near-term quantum devices. The security of his protocol, however, relies on non-standard complexity-theoretic conjectures which were not previously studied in the literature. In this work we provide strong complexity-theoretic evidence in support of these conjectures. In particular we prove two versions of Aaronson's conjectures unconditionally in a black-box Fourier sampling setting. This mirrors earlier complexity-theoretic evidence for quantum advantage, bringing the security of Aaronson's protocol up to the same level of evidence we have for quantum advantage from heavy output generation.