Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups

TL;DR

This paper demonstrates that a classical user can verify the quantum computation of a server to determine the order of a solvable group, a problem with exponential quantum speed-up, within an interactive proof system.

Contribution

It introduces an interactive proof protocol allowing a classical verifier to verify quantum computations for the order of solvable groups, bridging classical verification and quantum computation.

Findings

Classical verifier can verify quantum computations for solvable group order

The protocol enables efficient verification of problems with exponential quantum speed-up

Advances understanding of classical-quantum interactive proof systems

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.