Quantum superiority for verifying NP-complete problems with linear optics

TL;DR

This paper demonstrates that linear optics can be used to verify NP-complete problems, showcasing quantum superiority with simpler devices than universal quantum computers, and provides a feasible protocol tolerant to imperfections.

Contribution

It introduces a linear optics-based protocol for verifying NP-complete problems using quantum proofs, simplifying implementation and tolerating experimental imperfections.

Findings

Quantum proofs can be implemented with a single photon superposition.

Verification tests require only simple linear-optical transformations.

The protocol is robust against experimental imperfections.

Abstract

Demonstrating quantum superiority for some computational task will be a milestone for quantum technologies and would show that computational advantages are possible not only with a universal quantum computer but with simpler physical devices. Linear optics is such a simpler but powerful platform where classically-hard information processing tasks, such as Boson Sampling, can be in principle implemented. In this work, we study a fundamentally different type of computational task to achieve quantum superiority using linear optics, namely the task of verifying NP-complete problems. We focus on a protocol by Aaronson et al. (2008) that uses quantum proofs for verification. We show that the proof states can be implemented in terms of a single photon in an equal superposition over many optical modes. Similarly, the tests can be performed using linear-optical transformations consisting of a few operations: a global permutation of all modes, simple interferometers acting on at most four modes, and measurement using single-photon detectors. We also show that the protocol can tolerate experimental imperfections.