I Are electrons universal problem solvers?

[porton]

TL;DR Summary

Could knowing a wave function solve an NP-complete problem?

Existence of an universal problem solver, a polynomial-time NP-complete algorithm is a $1000000 prize question.

But suppose that we were able to know something "simple", e.g. an electron state or electron wave function exactly.

Would we be able to solve complex mathematical problems (like deciphering ciphers or quickly finding theorem proofs) by knowing these physical states?

Are electron wave function "decisions" (whether at a given point the wave function values are above or below a given number) an efficient NP-complete oracle even in the case if the electron is not a part of a computer (in the usual sense) running a polynomial-time NP-complete algorithm?

Suppose yes, then would from this and also simulation model of the universe follow than an electron is driven by an "all knowing" computer or maybe an NP-complete algorithm?

In other words, are electrons universal problem solvers?

Put another way: Suppose we can calculate an electron wave function for some not very long period of time (think of 10 seconds) exactly. Would it easily make us able to solve an NP-complete problem (decipher ciphers, find proofs of a math theorem just by entering into a computer its thesis, etc.) quickly (in polynomial time)?

Trying to formulate it with mathematical exactness: Suppose we have an oracle for decisions (whether at a given point the wave function values are above or below a given number) of wave functions specified as descriptions of function in ZFC for a time (in some measurement system like SI) up to a (binary) logarithm of a given natural number. Is this oracle a polynomial solution of an NP-complete problem?

 

[mfb]

"P" is polynomial time with a deterministic algorithm. We already know that nondeterministic systems might be different. That's the "N" in "NP"!

Simple wave functions can be solved exactly - the hydrogen atom is routinely solved in university courses. That has nothing to do with complexity classes.
If you could find the wave function of an arbitrary system efficiently with classical methods then you would make quantum computers unnecessary (it would imply P=BQP). How these are related to NP is an open question.

10 seconds is an extremely long time for an electron, by the way.

Suppose yes, then would from this and also simulation model of the universe follow than an electron is driven by an "all knowing" computer or maybe an NP-complete algorithm?

In other words, are electrons universal problem solvers?

These questions don't make sense. And note that there is nothing special about electrons in quantum mechanics.

 

[Demystifier]

In other words, the answer is - no.

 

[Vanadium 50]

Electrons are also used in classical computers. That's why we call it electronics.

 

[Jarek 31]

It seems the question concerns ways of using electrons in ways alternative to standard electronics (?) ... like quantum computers - for which there is still not known polynomial algorithm for NP.

Here is another alternative - NP complete problem (nondeterministic polynomial) can be transformed into search for a fixed point:
imagine a hardware implemented verifier for an instance of NP problem - which sends to own input the same if it solves the problem, "input+1" otherwise:

Such circuit with clock would test one possibility per cycle, finally reaching a satisfying input in exponential expected time.

But what if there is not clock?
We would get hydrodynamics of electrons, which fixed point solves our NP problem - could such electron flow stabilize faster than in exponential expected time?