  We show that a collection of lossy multi-chromatically modulated qubits can
be used to dissipatively engineer arbitrary Gaussian states of a set of bosonic
modes. Our ideas are especially suited to superconducting-circuit
architectures, where all the required ingredients are experimentally available.
The generation of such multimode Gaussian states is necessary for many
applications, most notably measurement-based quantum computation. We build upon
some of our previous proposals, where we showed how to generate single-mode and
two-mode squeezed states through cooling and lasing. Special care must be taken
when extending these ideas to many bosonic modes, and we discuss here how to
overcome all the limitations and hurdles that naturally appear. We illustrate
our ideas with a fully worked out example consisting of GHZ states, but have
also tested several other examples such as cluster states. All these examples
allow us to show that it is possible to use a set of N lossy qubits to cool
down a bosonic chain of N modes to any desired Gaussian state.
