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

• URL: http://arxiv.org/abs/2310.06034v1
• Date: Mon, 9 Oct 2023 18:00:04 GMT
• Title: Complexity of Gaussian quantum optics with a limited number of non-linearities
• Authors: Michael G. Jabbour and Leonardo Novo
• Abstract summary: We show that computing transition amplitudes of Gaussian processes with a single-layer of non-linearities is hard for classical computers. We show how an efficient algorithm to solve this problem could be used to efficiently approximate outcome probabilities of a Gaussian boson sampling experiment.
• Score: 4.532517021515834
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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