  We present a loop-based optical processor enabling time-domain programmable
beam-splitter (BS) operations for a phase-sensitive non-Gaussian state. The
loop itself is of high quality, allowing for storage of a non-Gaussian state
for up to seven round trips while preserving its Wigner negativity and phase
coherence. We perform various BS operations on a non-Gaussian state and
evaluate them as transformations of the state's waveforms. Our work integrates
non-Gaussian states with time multiplexing, laying the foundation for
large-scale universal quantum information processing.
