Over the past couple of years, I've been learning a little about the world of quantum machine learning (QML) and the sorts of things people are thinking about there. I recently gave an high-level talk on some of these ideas in connection to a December 2024 preprint called "Towards Structure-Preserving Quantum Encodings", coauthored with collaborators at Deloitte (Andrew Vlasic and Anh Pham) and MIT (Arthur Parzygnat). I spoke on this at the AWM Research Symposium this past May and have decided to write it up in a series of blog posts, as well.

In short, our preprint translates one aspect of an open problem in QML into the language of category theory, in hopes that by casting the problem in a more mathematically-formal light, we might be led to new tools and techniques that could help. I'll explain that in this series of articles.

Of course, the real question is: Did this help the QML problem? Right now, it's too early to know. Our preprint was written to a QML audience, and we assumed no familiarity with category theory. Still, it takes a while for ideas to spread. So, one goal for writing this series is just to get these ideas "out there" and see if they're of interest to anybody.

Another goal is just to share with everyone some topics that I personally think are interesting.

So here we go!