**Title:** Quantum materials and quantum computing: new approaches inspired by pure mathematics

**Speaker:** Dr. Steven Rayan, Director, Centre for Quantum Topology and Its Applications (quanTA) and Professor, Mathematics and Statistics, University of Saskatchewan (https://researchers.usask.ca/steven-rayan/#top)

**Location: **HP 4351 (MacPhail Room) – Carleton University

**Time:** Wednesday March 13, 2024 (4:00 pm – 5:30 pm)

**Note**: There will be a coffee break before the talk starting at 3:30 pm in the Faculty Lounge near MacPhail Room.

**Abstract: **The advent of topological materials, a form of physical matter with unusual but useful properties, has brought with it unexpected new connections between pure mathematics on the one side and physics, chemistry, and material science on the other side. As the name suggests, topology has played a significant role in understanding and classifying these materials. In this talk, I will offer a brief look at a vast extension to this story, arising from my work as a pure mathematician in collaboration with a number of individuals from the physical sciences over the last four years. In this work, geometry and representation theory — in particular, the complex algebraic geometry of Riemann surfaces and the representation theory of Fuchsian groups — anticipates a new form of quantum matter, dubbed “hyperbolic quantum matter”. Remarkably, this matter has been engineered synthetically by various groups. I will connect this development to another major technological revolution of recent years, that of quantum computing. In the quanTA Centre here at USask, which brings together mathematicians and other scientists, we have been experimenting with quantum computing techniques in the context of problems such as RNA folding. However, in general terms, quantum computing technologies are not yet scalable and are not yet fault tolerant. This brings us back to hyperbolic quantum matter: qubits based on hyperbolic quantum materials yield the possibility of new ways of generating quantum logic gates and of protecting the coherence of quantum states, which may in turn help with scaling up and enhancing the signal-to-noise ratio of quantum machines. We will take a tour through all of these developments — and there will be lots of pictures.