  We present a procedure to construct tensor-network representations of
many-body Gaussian states efficiently and with a controllable error. These
states include the ground and thermal states of bosonic and fermionic quadratic
Hamiltonians, which are essential in the study of quantum many-body systems.
The procedure improves computational time requirements for constructing
many-body Gaussian states by up to five orders of magnitude for reasonable
parameter values, thus allowing simulations beyond the range of what was
hitherto feasible. Our procedure combines ideas from the theory of Gaussian
quantum information with tensor-network based numerical methods thereby opening
the possibility of exploiting the rich tool-kit of Gaussian methods in
tensor-network simulations.
