  Frequency-encoded quantum information offers intriguing opportunities for
quantum communications and networking, with the quantum frequency processor
paradigm -- based on electro-optic phase modulators and Fourier-transform pulse
shapers -- providing a path for scalable construction of quantum gates. Yet all
experimental demonstrations to date have relied on discrete fiber-optic
components that occupy significant physical space and impart appreciable loss.
In this article, we introduce a model for the design of quantum frequency
processors comprising microring resonator-based pulse shapers and integrated
phase modulators. We estimate the performance of single and parallel
frequency-bin Hadamard gates, finding high fidelity values that extend to
frequency bins with relatively wide bandwidths. By incorporating multi-order
filter designs as well, we explore the limits of tight frequency spacings, a
regime extremely difficult to obtain in bulk optics. Overall, our model is
general, simple to use, and extendable to other material platforms, providing a
much-needed design tool for future frequency processors in integrated
photonics.
