  Linear canonical transformations of bosonic modes correspond to Gaussian
unitaries, which comprise passive linear-optical transformations as effected by
a multiport passive interferometer and active Bogoliubov transformations as
effected by a nonlinear amplification medium. As a consequence of the
Bloch-Messiah theorem, any Gaussian unitary can be decomposed into a passive
interferometer followed by a layer of single-mode squeezers and another passive
interferometer. Here, it is shown how to circumvent the need for active
transformations. Namely, we provide a technique to simulate sampling from the
joint input and output distributions of any Gaussian circuit with passive
interferometry only, provided two-mode squeezed vacuum states are available as
a prior resource. At the heart of the procedure, we exploit the fact that a
beam splitter under partial time reversal simulates a two-mode squeezer, which
gives access to an arbitrary Gaussian circuit without any nonlinear optical
medium. This yields, in particular, a procedure for simulating with linear
optics an extended boson sampling experiment, where photons jointly propagate
through an arbitrary multimode Gaussian circuit, followed by the detection of
output photon patterns.
