  Non-Gaussian quantum states of light are critical resources for optical
quantum information processing, but methods to generate them efficiently remain
challenging to implement. Here we introduce a generic approach for non-Gaussian
state production from input states populating discrete frequency bins. Based on
controllable unitary operations with a quantum frequency processor, followed by
photon-number-resolved detection of ancilla modes, our method combines recent
developments in both frequency-based quantum information and non-Gaussian state
preparation. Leveraging and refining the K-function representation of quantum
states in the coherent basis, we develop a theoretical model amenable to
numerical optimization and, as specific examples, design quantum frequency
processor circuits for the production of Schr\"{o}dinger cat states, exploring
the performance tradeoffs for several combinations of ancilla modes and circuit
depth. Our scheme provides a valuable general framework for producing complex
quantum states in frequency bins, paving the way for single-spatial-mode,
fiber-optic-compatible non-Gaussian resource states.
