Besides machine learning, quantum info theory, optimization, and statistics knowledge, what are the prerequisites to implement existing ML techniques and create new ML techniques that would work on a quantum computer and be optimized to take full advantage of quantum computing’s efficiencies? What courses does one need to take? I don’t mean simulating quantum computers on a classical computers. I mean actually doing ML or Statistics or Topological data analysis on a trapped ion quantum computer.
Quantum Machine Learning (QML) is both young and highly cross-disciplinary, meaning that it will be hard to find courses in specific disciplines (math, physics, computer science, etc) that provide background tailored to the subject.
One way to approach the field is to work backwards, by first choosing a specific type of algorithm that's currently popular and then find out what tools you need to understand whats going on. The background required to work with QAOA/quantum annealing/adiabatic algorithms is different than that required to work with qRAM-related things like HHL, qPCA (dequantized!), and working on any of those algorithms in a theoretical sense is very different than running on real hardware and interpreting the results.
A couple of questions that might help you narrow your interests are:
If after deciding on a more specific QML approach you are still unsure of the kind of background necessary, come back and ask questions about that problem/algorithm and you'll have an easier time finding specific answers.