Gaussian Boson Sampling using threshold detectors

Understand

We study what is arguably the most experimentally appealing Boson Sampling architecture: Gaussian states sampled with threshold detectors.

• We show that in this setting, the probability of observing a given outcome is related to a matrix function that we name the Torontonian, which plays an analogous role to the permanent or the Hafnian in other models.
• We also prove that, provided that the probability of observing two or more photons in a single output mode is sufficiently small, our model remains intractable to simulate classically under standard complexity-theoretic conjectures.
• Finally, we leverage the mathematical simplicity of the model to introduce a physically motivated, exact sampling algorithm for all Boson Sampling models that employ Gaussian states and threshold detectors.