Algebraic Graph Theory and Quantum Computing


News


Next lecture

Just a draft.


Assignments

You are not expected to solve all problems from the three sets that I will post, and the choice is largely up to you (provided they are spread reasonably evenly over the sets). Any correct solution submitted will earn 5 marks (unless otherwise noted). If the solution is essentially correct and you will learn nothing by fixing it, you will earn 4 marks. Otherwise your solution will be returned so you can rewrite it. If your solution is not easily readable, the same procedure applies. When you submit a correct and/or readable solution, you will then earn 4 marks. There could be more than one iteration in this process.

Submit your solutions to Mariia via crowdmark.

Bonus marks will be awarded and I am prepared to be generous (but if you are going to put in lot of extra work, check with me first). You have the option of replacing up to 10 problems by a course-related project (which might involve computation). Collaboration on a project might be permitted. The initiative is up to you and the details will have to be agreeable to both of us.

Solution to problems may make use of results from other problems, even if you have not solved them. If you find a solution to a problem in notes or online, you may base your solution on it. You must however use notation from the course, and your solution must be self-contained. Of course you should also cite your source.

I do not want collaboration on the problems. I will be happy to discuss them in class or in person.


Useful Material

Text books and Notes: in each case, parts of the source cited may be useful, but the course will not be based on any one of these.

  1. Variations on Theme: Graph Homomorphisms. (David Roberson's Ph. D. thesis.)
  2. Quantum Homomorphisms. (Godsil, unpublished notes)
  3. Algebraic Graph Theory. (Godsil and Royle - Springer 2001)
  4. Linear Algebra. (Peter D. Lax - Wiley 1977)
  5. Discrete Quantum Walks on Graphs and Digraphs. (Godsil and Zhan - CUP 2023)
  6. Graph Spectra and Continuous Quantum Walks. (Godsil and Coutinho, draft of a text).
  7. More Linear Algebra. (Godsil, unpublished notes)
  8. Discrete Quantum Walks on Graphs and Digraphs. (Hanmeng Zhan's Ph. D. thesis.)
  9. An Invitation to Arithmetic Geometry. (Dino Lorenzini - AMS 1996) Possibly useful for algebraic number theory - it is a nice book, but could be a bit advanced. However the alternatives are two or three times the price.

Recordings of lectures on:

  1. Combinatorics and Quantum Walks
  2. Quantum Morphisms
  3. Linear Algebra and Combinatorics.


Contact

If you google on my name, you will reach my webpage very quickly.


Fields web page for the course.

Here. There is information there not repeated above.