Some students in my department this quarter hosted a reading group on quantum computing. Quantum computing is becoming more and more relevant and the topic attracted the participation of a diverse group of researchers. The best way to handle the scope of the topic and diversity of the participants was to invite volunteer speakers to give talks on the quantum analog of their own research area — “Quantum Circuit Lower Bounds,” “Quantum Game Theory,” and “QPSPACE” were among some of the topics. Naturally, I saw this as a great opportunity to understand more about quantum spectral graph theory. In this post I will outline some basic definitions and properties of quantum graphs, and as a follow up to my previous post on the connections between spectral geometry and graph theory, discuss isospectral properties of discrete and quantum graphs. Continue reading →