On Certified Randomness from Fourier Sampling or Random Circuit Sampling

TL;DR

This paper introduces a quantum Fourier Sampling-based protocol for certified randomness in the quantum random oracle model, providing a non-computational security proof and supporting Aaronson's conjectures for RCS-based randomness.

Contribution

It presents a publicly verifiable certified randomness protocol in the QROM using Fourier Sampling, independent of computational assumptions, and extends Aaronson's conjectures via a Fourier Sampling version.

Findings

Protocol achieves black-box security without computational assumptions.

Supports Aaronson's conjectures through Fourier Sampling and complexity-theoretic separation.

Complementary to existing protocols, with exponential-time classical verification.

Abstract

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 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'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, 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.