Math Is Fun Forum

iiooasd1217

Novice

Registered: 2023-10-31

Posts: 7

Quantum Computers Breaking Computability

I figured this out around a year ago and was too lazy to make a paper. I thought I would post it here instead. Have fun with existential dread!

Alan Turing was one of the best minds in history. In his days he wrote a paper regarding the incompleteness theory. This theory said that maths was incomplete. Turing proved this with a thought experiment. Imagine an algorithm T(x) that would tell you if an algorithm, x, was complete (0 if incomplete 1 if complete). Now imagine an algorithm U(x) that always does the opposite result of T. When you put T(U)  you will get a paradox where T outputs both a 1 and a 0. That's impossible... Right?

NO!!!

Try this same problem with a quantum algorithm. What do you get? A working system! The system would have a qbit with a superposition between 1 and 0! Do quantum particles break maths?

Thank you for reading this sorta-rant. Enjoy your existential dread. Good luck!

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I'll do a^2+b^2=c^2. I'll even do pir^2. But y=mx+b is where I draw the line.
Why do people become maths teachers? Because they have problems.