Experimental demonstration of quantum advantage for NP verification with limited information

TL;DR

This paper demonstrates experimentally that a quantum verifier can efficiently verify NP-complete problems with limited information, showing a clear advantage over classical methods in a specific proof verification scenario.

Contribution

It provides the first experimental demonstration of quantum advantage in NP verification with limited information using a simple linear optical setup.

Findings

Quantum verifier efficiently checks NP problems with limited proof information.

Classical computers would take much longer to perform the same verification.

Experimental implementation is feasible within seconds using linear optics.

Abstract

In recent years, many computational tasks have been proposed as candidates for showing a quantum computational advantage, that is an advantage in the time needed to perform the task using a quantum instead of a classical machine. Nevertheless, practical demonstrations of such an advantage remain particularly challenging because of the difficulty in bringing together all necessary theoretical and experimental ingredients. Here, we show an experimental demonstration of a quantum computational advantage in a prover-verifier interactive setting, where the computational task consists in the verification of an NP-complete problem by a verifier who only gets limited information about the proof sent by an untrusted prover in the form of a series of unentangled quantum states. We provide a simple linear optical implementation that can perform this verification task efficiently (within a few seconds), while we also provide strong evidence that, fixing the size of the proof, a classical computer would take much longer time (assuming only that it takes exponential time to solve an NP-complete problem). While our computational advantage concerns a specific task in a scenario of mostly theoretical interest, it brings us a step closer to potential useful applications, such as server-client quantum computing.