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).
Such problem can be for example finding a divisor (RSA breaking) or finding a key that if we use it to decrypt the beginning of the file, there will be significant correlations (brute force attack).
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 the 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.
If not, it's no longer classical computer: while removing the clock/synchronization we are destroying the order and releasing all it's statistical, quantum properties to make what physics do the best: solve its partial differential equations. Now it became continuous and so it can go with energy gradient to some local minimum, but the only local minimals are stable states (solutions). Every other is extremely unstable - electron fluid won't rest until it find a solution. The statistics, differences between propagation times will create extremely fast chaotic search for it.
Thanks of being continuous and using natural physics property to solve partial differential equations, it could make some short path to find the solution. (?)
I imagine it as a river of electrons, which goes around because of 'pomps' in logical gates and wants to minimize 'energy of turbulences'. We could manipulate voltage to make something like simulated annealing to help with stabilization.
Eventually if it would make a quantum computer this way, we would 'feed' it with entangled all possible inputs and the amplitude of all but stable solutions should vanish.
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 idea comes from the idea of time-loop computers: there are some reasons to believe that that physics can allow to make a prediction in microscale. If we could predict that in let say nanosecond will be absorbed a photon, we could transfer data back in time. If we would use it to close such causality loop, physics should stabilize if it can, to prevent paradoxes. If it's not possible it should break the weakest link - make that the prediction would go wrong.