## Organization

We (Hanmeng Zhan, Chris Godsil, Gabriel Coutinho) will hold an on-line course on quantum walks in Winter 2021. There will be two lectures each week, usually offered by Gabriel and Harmony. The intended audience is entering graduate students. The background requirement is some knowledge of graph theory and a thorough understanding of linear algebra. Many of the lectures will based on the following drafts of books:

- Graph Spectra and Continuous Quantum Walks, Coutinho and Godsil.
- Discrete Quantum Walks, Godsil and Zhan.

It might be possible to get credit from your institution for taking this course. If they charge you a fee, they can pay for grading. :-)

## Schedule

Lectures are on zoom, Tuesdays and Thursdays 11:00am, starting January 12.

Recordings of the lectures: (GC= Gabriel, continuous walks. HZ=Harmony, discrete walks.)

## Exercises

## Content and Outline

We will focus on the mathematical aspects of quantum walks. The course will cover both discrete and continuous walks, on a more or less equal footing. Possible topics:

- motivation
- Physics
- arc-reversal walks
- representation theory for two reflections
- Grover
- face-vertex walks
- bipartite walks and Hamiltonians
- graph isomorphism failures
- real states (periodicity, state transfer, ratio condition)
- pst on Laplacians of trees
- cubelike graphs
- strongly cospectral vertices and symmetries
- uniform mixing on cycles
- orthogonal polynomials
- pretty good state transfer
- fractional revival
- average mixing, average states

## Contact

For further information, contact Chris Godsil.