  We develop a quantum theory describing the input-output properties of
Josephson traveling wave parametric amplifiers. This allows us to show how such
a device can be used as a source of nonclassical radiation, and how dispersion
engineering can be used to tailor gain profiles and squeezing spectra with
attractive properties, ranging from genuinely broadband spectra to "squeezing
combs" consisting of a number of discrete entangled quasimodes. The device's
output field can be used to generate a multi-mode squeezed bath--a powerful
resource for dissipative quantum state preparation. In particular, we show how
it can be used to generate continuous variable cluster states that are
universal for measurement based quantum computing. The favourable scaling
properties of the preparation scheme makes it a promising path towards
continuous variable quantum computing in the microwave regime.
