Let's say I have a way to represent $N$ bits such that those bits are in a superposition of the $2^N$ possible states those bits can have and that I can do XOR and AND on those superpositional bits to be able to map $N$ superpositional input bits to $M$ superpositional output bits using any logical circuit (since XOR and AND are supported).
Let's say that I am also able to include bits in those logic circuits which are not superpositional but have specific values of either 0 or 1. This way I can do a NOT by XORing a superpositional bit by 1 for example.
At the end of the logic circuit when I have the superpositional result, I can then decide what values the input bits had, and get a non superpositional result out for those inputs, without evaluating the circuit again. I can interpret the result as many times as I want for the entire permutation of input bits if I want to.
I'm wondering, would a superpositional logic technique like this be useful, and does anyone know if any work has been done in this area?
I know this is similar to how quantum computing works, except for a few key differences like not having interference, nor having probabilities for states, but it does allow cloning of the superpositional result, unlike quantum computing which only allows one question to be asked of the result.
I can think of a couple usage cases, but am wondering if there are others?
- Using a superpositional result as a way of letting an untrusted person specify how inputs should map to outputs (basically, "script" some process), without havign to sandbox the logic, worry about division by zero, infinite loops, and the like.
- I have yet to experiment deeply with this, but if you need to know several values of some function $f(x)$, it may be more computationally efficient to evaluate it superpositionally and then re-interpret the superpositional result several times, versus just calculating the function several times.