Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups
Quantum Physics
2021-10-05 v1 Computational Complexity
Abstract
In this paper we consider what can be computed by a user interacting with a potentially malicious server, when the server performs polynomial-time quantum computation but the user can only perform polynomial-time classical (i.e., non-quantum) computation. Understanding the computational power of this model, which corresponds to polynomial-time quantum computation that can be efficiently verified classically, is a well-known open problem in quantum computing. Our result shows that computing the order of a solvable group, which is one of the most general problems for which quantum computing exhibits an exponential speed-up with respect to classical computing, can be realized in this model.
Cite
@article{arxiv.1805.03385,
title = {Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups},
author = {François Le Gall and Tomoyuki Morimae and Harumichi Nishimura and Yuki Takeuchi},
journal= {arXiv preprint arXiv:1805.03385},
year = {2021}
}
Comments
13 pages