  We introduce a new family of quantum circuits in Continuous Variables and we
show that, relying on the widely accepted conjecture that the polynomial
hierarchy of complexity classes does not collapse, their output probability
distribution cannot be efficiently simulated by a classical computer. These
circuits are composed of input photon-subtracted (or photon-added) squeezed
states, passive linear optics evolution, and eight-port homodyne detection. We
address the proof of hardness for the exact probability distribution of these
quantum circuits by exploiting mappings onto different architectures of
sub-universal quantum computers. We obtain both a worst-case and an
average-case hardness result. Hardness of Boson Sampling with eight-port
homodyne detection is obtained as the zero squeezing limit of our model. We
conclude with a discussion on the relevance and interest of the present model
in connection to experimental applications and classical simulations.
