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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