## Smith Colloquium

### March 25, 2021

### Zhenghan Wang, University of California Santa Barbara

*Title*: **Mathematics of topological quantum computing **

*Abstract*: In topological quantum computing, information is encoded in "knotted" quantum states of topological phases of matter, thus solving the fragility of the qubits at the hardware level. Information is encoded non-locally into topological invariants that spread into local quantities just as the Euler characteristic spreads into local curvature in the Gauss-Bonnet theorem. Nature does provide such topological invariants in topological phases of matter such as the fractional quantum liquids and topological insulators. I will start with an introduction to topological quantum computing and then discuss some inspired quantum mathematics centering on the classification of topological phases of matter.