Pré-Publication, Document De Travail Année : 2023

Complexity of Gaussian quantum optics with a limited number of non-linearities

Résumé

It is well known in quantum optics that any process involving the preparation of a multimode gaussian state, followed by a gaussian operation and gaussian measurements, can be efficiently simulated by classical computers. Here, we provide evidence that computing transition amplitudes of Gaussian processes with a single-layer of non-linearities is hard for classical computers. To do so, we show how an efficient algorithm to solve this problem could be used to efficiently approximate outcome probabilities of a Gaussian boson sampling experiment. We also extend this complexity result to the problem of computing transition probabilities of Gaussian processes with two layers of non-linearities, by developing a Hadamard test for continuous-variable systems that may be of independent interest. Given recent experimental developments in the implementation of photon-photon interactions, our results may inspire new schemes showing quantum computational advantage or algorithmic applications of non-linear quantum optical systems realizable in the near-term.

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Dates et versions

hal-05022355 , version 1 (06-04-2025)
hal-05022355 , version 2 (21-08-2025)

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Michael G Jabbour, Leonardo Novo. Complexity of Gaussian quantum optics with a limited number of non-linearities. 2025. ⟨hal-05022355v1⟩
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