Let's take some NP-problem: we have a verifier which can quickly say that given input is correct or not, but there is huge number of possible inputs and we want to tell if there is a correct one (find it).
Imagine we have a chip with 'input' and 'output' in which is implemented (e.g. FPGA):
IF 'input' verifies the problem
- THEN send 'input' to 'output'
- ELSE send next possible 'input' (cyclically) to 'output'
such that this chip uses only basic logic gates - computations are made in some small number of layers - IT DOESN'T USE CLOCK (we can do it for some NP problems like 3SAT).
Now connect it's 'output' and 'input' to make a loop.
Such loop will be stable if it has found a solution (which can be transferred out). If there would be a clock, in each cycle there would be checked one input. But without clock it should be pure hydrodynamics of electrons. If there is a solution, other states would create fluctuations in time
- should be less energetically preferred than the stable one - physics should quickly solve our problem.
I know - there can be a problem with nonlinearity of transistors? If yes, there are plenty of technologies, maybe some of them would handle with it?
This loop computer idea is practically simplified from time-loop computer idea: