  Invertible Neural Networks (INN) have become established tools for the
simulation and generation of highly complex data. We propose a quantum-gate
algorithm for a Quantum Invertible Neural Network (QINN) and apply it to the
LHC data of jet-associated production of a Z-boson that decays into leptons, a
standard candle process for particle collider precision measurements. We
compare the QINN's performance for different loss functions and training
scenarios. For this task, we find that a hybrid QINN matches the performance of
a significantly larger purely classical INN in learning and generating complex
data.
