Gaussian Boson Sampling using threshold detectors

TL;DR

This paper investigates Gaussian Boson Sampling with threshold detectors, introducing the Torontonian matrix function, demonstrating classical intractability under certain conditions, and providing an exact sampling algorithm for such models.

Contribution

It introduces the Torontonian as a key matrix function, proves classical intractability under specific conditions, and develops an exact sampling algorithm for Gaussian Boson Sampling with threshold detectors.

Findings

Probability linked to the Torontonian matrix function.

Model remains classically intractable under certain photon detection conditions.

Provides an exact sampling algorithm for Gaussian Boson Sampling with threshold detectors.

Abstract

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.