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Topology of course is fundamental to all of physics, but in that context my guess would be on topological quantum computing: https://en.wikipedia.org/wiki/Topological_quantum_computer

I once attended a talk on the subject by Michael Freedman who is with Microsoft Station Q. They are trying to build just such a computer.



Since you didn't include it, but it's relevant to the topic at hand -- Michael Freedman is also a Fields medalist that did substantial work in topology. Which is, ultimately, why he's involved with Station Q -- he was part of the group that realized you could use the topological structure of certain interactions to encode general computations, and was part of convincing MS to pursue that.

https://en.wikipedia.org/wiki/Michael_Freedman


Vladimir Voevodsky's legacy could be part of Quantum Computer design if it pans out in the future.


It is actually Michael Freedman who was that math panel. https://youtu.be/d7f_GZsQMpA?t=59m56s

Not sure who else might have a device that can instantiate in some physical way a Quantum Superposition, but Microsoft showed such a device during that discussion: https://youtu.be/d7f_GZsQMpA?t=1h3m6s




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