Zhenghan Wang, UCSB & Microsoft Station Q

Title: Topology and algebra in quantum computing and physics

Abstract: Elementary errors in topological quantum codes and elementary excitations in topological phases of matter form an interesting mathematical structure: a unitary modular tensor category in mathematics, and an anyon model in physics.  I will explain this occurrence, and some resulting mathematics in quantum topology and quantum algebra.  An argument will be made that topology is inevitable for building a utility scale fault-tolerant quantum computer, which is becoming an engineering problem of system architecture and control.  As AI is reshaping mathematics, and many of us are wondering what is left for us. The discovery, formulation, and study of universal deep patterns in the world---natural or man-made---will remain.  This episode is an instance that arose from topological fault-tolerance in quantum computing.