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Journal Articles npj Quantum Information Year : 2018

Quantum superiority for verifying NP-complete problems with linear optics

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.

Dates and versions

hal-01671939 , version 1 (22-12-2017)

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Juan Miguel Arrazola, Eleni Diamanti, Iordanis Kerenidis. Quantum superiority for verifying NP-complete problems with linear optics. npj Quantum Information, 2018, ⟨10.1038/s41534-018-0103-1⟩. ⟨hal-01671939⟩
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