I hold a DPhil (aka PhD) from the Department of Computer Science at the University of Oxford. I was based in the Quantum Compuer Science research group, which works on and with some neat graphical languages. With these, we can use diagrams to figure out things about quantum mechanical systems, particularly “quantum computers”. One of my supervisors liked to call it “kindergarten quantum mechanics”, because you don’t really need any mathematical knowledge to use these languages. You just need to know a few rules about how to replace bits of the diagram with other things.
My research focussed on developing techniques for doing (semi-)automated reasoning with these languages - in other words, getting a computer to both do some of the more tedious work of using the diagrams, and checking that your manipulations are correct. In particular, my work was on representing infinite families of rules in a finite way, so they can actually be used by a computer. There is a tool (Quantomatic) that implements this work.
I previously did a four-year undergraduate Masters in Mathematics and Computer Science, also at the University of Oxford. I did a project in my final year (in the same research group as my DPhil), creating a little program to do some (very) basic diagram simplification for a particular graphical language. You can read my project report if you like.