  A growing cohort of experimental linear photonic networks implementing
Gaussian boson sampling (GBS) have now claimed quantum advantage. However, many
open questions remain on how to effectively verify these experimental results,
as scalable methods are needed that fully capture the rich array of quantum
correlations generated by these photonic quantum computers. In this paper, we
briefly review recent theoretical methods to simulate experimental GBS
networks. We focus mostly on methods that use phase-space representations of
quantum mechanics, as these methods are highly scalable and can be used to
validate experimental outputs and claims of quantum advantage for a variety of
input states, ranging from the ideal pure squeezed vacuum state to more
realistic thermalized squeezed states. A brief overview of the theory of GBS,
recent experiments and other types of methods are also presented. Although this
is not an exhaustive review, we aim to provide a brief introduction to
phase-space methods applied to linear photonic networks to encourage further
theoretical investigations.
