We count things with numbers classically. But in the quantum world, such as electrons in a material, the distinction between one thousand electrons and two more could be blurred by quantum superposition. As a result, quantum counting is better done using wave functions. It turns out that information can be processed much more efficiently using wave functions on quantum computers. I will explain the basics of wave functions, quantum computing, and speculate on implications for future mathematics.

Zhenghan Wang was born in Tsingtao, China and received his Ph.D in mathematics from UCSD in 1993. He was an assistant Professor of Mathematics at University of Michigan from 1993–1996 and Professors of Mathematics at Indiana University at Bloomington from 1996–2007 (1996–1997 on leave as an NSF postdoc at UCSD and 2005–2007 on leave at Microsoft). He is now a Professor of Mathematics at UCSB since 2012 and a Distinguished Visiting Research Chair at Perimeter Institute for Theoretical Physics since 2013. He has been a researcher at Station Q since 2005. His main interests are quantum mathematics, theoretical models of topological phases of matter, and their application to quantum physics and quantum computing.

Department of Mathematics Colloquium

Researchers should cite this work as follows:

• Zhenghan Wang (2020), "Quantum Mathematics: Counting, Computing, and Reasoning with Quantum Numbers," https://nanohub.org/resources/34637.

  BibTex | EndNote

1. majoranas
2. non-abelian anyons
3. quantum computing
4. quantum science and information
5. topology