  An open question in quantum optics is how to manipulate and control complex
quantum states in an experimentally feasible way. Here we present concepts for
transformations of high-dimensional multi-photonic quantum systems. The
proposals rely on two new ideas: (I) a novel high-dimensional quantum
non-demolition measurement, (II) the encoding and decoding of the entire
quantum transformation in an ancillary state for sharing the necessary quantum
information between the involved parties. Many solutions can readily be
performed in laboratories around the world, and identify important pathways for
experimental research in the near future. The concept has been found using the
computer algorithm Melvin for designing computer-inspired quantum experiments.
This demonstrates that computer algorithms can inspire new ideas in science,
which is a widely unexplored potential.
