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The digital ising thing was a very interesting line of research that Fujitsu has been trying to sell for 10 years or so: https://www.fujitsu.com/global/services/business-services/di...

They presented their v1 chip architecture at ISSCC in 2015 much to the consternation of a few quantum computing people who (rightly) objected to the characterization of it as an "Ising" chip, because it cannot represent superposition.

It's a pretty cool sort of system that should be able to solve pseudo-energy-minimization problems, but they are only theoretically sound when energy minimization corresponds to minimizing a Lyapunov function. Sadly, it's not clear that there is a way to generically construct a Lyapunov function with a minimum that corresponds to an NP-complete problem. The Fujitsu device supposedly is good at "easy" versions of problems, but so is a SAT solver.




The Fujitsu device is a synchronous digital architecture. I'm using asynchronous oscillators, more like Lo et. al. (https://www.nature.com/articles/s41593-024-01607-5)

I personally think it's super cool that we can replicate analog coupling dynamics using asynchronous digital logic!


I hate to burst your bubble, but when you do the dynamic systems math, they are sadly equivalent. You are working in the continuous time domain while the synchronous devices are working in the discrete time domain.


In practice, though, asynchronous systems can run a lot faster than their synchronous counterparts! Also, I'm mostly working on this project because it's cool and interesting to build oscillator-based computing systems on FPGAs, not because I'm trying to build a practical system.

That's why I posted it here: it's a fun use-case for asynchronous stuff you can do on FPGAs.


Yeah, it's nice to go faster, but "faster" will not outrace P != NP.

In all seriousness, I'm hoping that "Lyapunov computing" will get some more theoretical attention, because it is very easy to simulate extremely complicated dynamic systems (not constraining yourself to linked oscillator systems), but quantum computing has sort of sucked the air out of the "alternative computing technologies" ecosystem. In any case, the circuits have far outpaced the development of theory in this area.




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