## More about the Schrödinger equation on a finite graph

January 13, 2011 by Qiaochu Yuan

It looks like the finite graph model is not just a toy model! It’s called a continuous-time quantum random walk and is used in quantum computing in a way similar to how random walks on graphs are used in classical computing. The fact that quantum random walks mix sooner than classical random walks relates to the fact that certain quantum algorithms are faster than their classical counterparts.

I learned this from a paper by Lin, Lippner, and Yau, Quantum tunneling on graphs, that was just posted on the arXiv; apparently the idea goes back to a 1998 paper. I have an idea about another sense in which the finite graph model is not just a toy model, but I have not yet had time to work out the details.

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on October 17, 2022 at 4:33 pm |autoThere is another toy model that caught my attention recently in the setting of vector spaces over $\mathbb{Z}_2$. Might interest you!

https://www.ellerman.org/book-draft-quantum-mechanics-over-sets/

on January 14, 2011 at 11:06 am |science and mathThanks for the update on the topic.