Compilation of useful posts from around the WWW to start learning the incredibly rich set of mathematics needed to understand Quantum Mechanics, Quantum Computation, Neural Networks, Deep Learning, and AI in general. Quantum AI is pretty brand new, and the math even more so. An exotic topic choice - but also an immensely rich and beautifully constructed universe/multiverse.
This is further broken down, as I show below, by the following subtopics that are prominent in machine learning.
BUT…these topics are best learned in context. Please do not jump into these topics without first building a real-world application (if you’re a Data Scientist) or at least some functioning code (if you’re a researcher). Machine learning success doesn’t happen by memorizing a knowledge-base of fundamentals devoid of real-world context. Since you mentioned for research, you can use the latter approach.
Begin by writing code that solves a problem, and use these mathematical concepts when and where they can help you. This will ensure you learn how these concepts help in real situations.
(current topics submitted by the machine learning community)