Quantum superiority for verifying NP-complete problems with linear optics

Juan Miguel Arrazola,Eleni Diamanti,Iordanis Kerenidis

doi:10.1038/s41534-018-0103-1

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.

Highlights

Quantum mechanics offers unprecedented possibilities to transmit and process information that have the potential to revolutionize information and communication technologies
It has been fruitful to focus on specific physical systems and search for tasks that are well suited to be deployed in such platforms and where a quantum advantage can be demonstrated
On the road to achieving universal quantum computing, it has become interesting to study specific tasks, notably Boson Sampling,[13,14,15,16,17,18] where a computational advantage may be demonstrated by a linear optics scheme that is simpler to implement than a universal quantum computer

Summary

INTRODUCTION

Quantum mechanics offers unprecedented possibilities to transmit and process information that have the potential to revolutionize information and communication technologies. In the case of verification where the revealed information is restricted, it might in principle be possible that quantum proofs can be verified more efficiently than classical ones, giving rise to a computational advantage. In a linear-optical setting, this state can quantum circuit, but involves an interaction between two parties; be implemented in terms of a single photon in a superposition the quantum superiority is not for solving a computational over N different modes as task but for verifying efficiently the solution of a computationally hard problem

RESULTS

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