I'm been trying to build a digital equivalent of quantum computer but notice a curious result.
The quantum 'logic gates' I have cannot in any shape or manner computer a trancendental number directly. Which is a bit pathetic, since that is a high priority.
But then I notice none of the quantum computer bits that make up our universe can compute transcendental numbers either. They at best perform integration operations which results in an indirect computation of trancendental numbers. E.g. charging of a capacitor by electrons - the rising voltage function is an integral and is given by a trancendental involving exp() function, but the make up of the capacitor and electron filling scheme is fundamentally a quantum process.
Wherever I look, the same pattern repeats. Each potential trancendental candidate is just an integration of quantum fluctions - verifying never does nature directly use trancentals in any form of quantum computing. Reality is weird. If true, then it is an incomprehensible result.
Why should nature have such a huge aversion to trancendentals?
The short and curlies of this result is that if quantum computers cannot in any way or shape compute with trancendentals by supposition of states, then there is no way to build a real quantum computers that solve a large percentage of real world problems in any useful way. There are deep flaws in "supposition of states" argument. A. It is false B. If true, conditions conditions are attached such as supposition of all states EXCEPT trancendentals. Which is fscking useless defintion from a mathematical and physics point of view.
Supposition of states should be replaced with "toggling between known states". That would then exclude trancendentals because it isn't a precise state which implies its not a valid state either.