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"Topological views on computational complexity", Michael Freedman, 1998

Reviewed July 27, 2023

Citation: Freedman, M. "Topological views on computational complexity." Documenta Mathematica-Extra Volume ICM (1998): 453-464.

Web: https://ems.press/books/dms/247/4751


This paper is the follow-up to Freedman's first paper on quantum computing,

> Freedman, Michael H. "P/NP, and the quantum field computer." Proceedings of the National Academy of Sciences 95.1 (1998): 98-101.

It is filled to the brim with fun ideas and philosophical musings. It is longer (12 pages) and more in-depth than the original, giving a more refined picture of potential quantum computation methods.

This paper is still early enough for there to be no Kitaev reference. It's purely a Freedman brain-child. While definitely a fun read, I don't think that this paper ended up being that fundamental. The big idea in mind seems to be "let's try to understand logic and computational complexity via a topological perspective on P/NP" - the end goal was understanding and philosophy. Pretty quickly the end goal turned into "let's make a cool computer", which works just as well.

A funny note: this paper has 31 citations, 23 of which are Louis Kauffman.