  We introduce a framework for simulating, on an $(n+1)$-qubit quantum
computer, the action of a Gaussian Bosonic (GB) circuit on a state over $2^n$
modes. Specifically, we encode the initial bosonic state's expectation values
over quadrature operators (and their covariance matrix) as an input
qubit-state. This is then evolved by a quantum circuit that effectively
implements the symplectic propagators induced by the GB gates. We find families
of GB circuits and initial states leading to efficient quantum simulations. For
this purpose, we introduce a dictionary that maps between GB and qubit gates
such that particle- (non-particle-) preserving GB gates lead to real
(imaginary) time evolutions at the qubit level. For the special case of
particle-preserving circuits, we present a BQP-complete GB decision problem,
indicating that GB evolutions of Gaussian states on exponentially many modes
are as powerful as universal quantum computers. We also perform numerical
simulations of an interferometer on $\sim8$ billion modes, illustrating the
power of our framework.
