We construct a constant-round zero-knowledge classical argument for NP secure against quantum attacks. We assume the existence of Quantum Fully-Homomorphic Encryption and other standard primitives, known based on the Learning with Errors Assumption for quantum algorithms. As a corollary, we also obtain a constant-round zero-knowledge quantum argument for QMA. At the heart of our protocol is a new no-cloning non-black-box simulation technique.
@article{arxiv.1912.04769,
title = {Post-quantum Zero Knowledge in Constant Rounds},
author = {Nir Bitansky and Omri Shmueli},
journal= {arXiv preprint arXiv:1912.04769},
year = {2020}
}