Assuming in the future there was a functioning 1024 qubit quantum supercomputer and it could run Shor's algorithm or Grover's algorithm to crack encryption very quickly. I'm interested in how the number of qubits translates to performance improvement over a regular 2 bit computer.
For example, if I used Shor's algorithm on a 4 qubit quantum supercomputer, would this take half the time to factor 1024 bit RSA as it would a regular 2 bit supercomputer? Then if we extrapolate upwards to 8 qubit supercomputer through to 512 qubit, 1024 qubit and even 2048 qubit etc. What sort of factorization speed increase would you get from adding more qubits? I originally thought quantum computers could have only 4 qubits. But it seems these days you can keep adding qubits up to the amount you want within technical reason. Does this mean if I had a 1024 qubit supercomputer I could factor RSA 1024 bit in a split second? At what speed could it check possible factorizations?
So I'm interested how long it would "theoretically" take to:
- Brute force find the key for a 1024 bit encrypted RSA message using Shor's algorithm.
- Brute force find the key for a 256 bit AES encrypted message using Grover's algorithm.
- Find a pre-image for a SHA2-512 bit hash.
- Construct a rainbow table for a SHA2-512 bit hash.
- If people are using 2048 bit RSA now as standard, will it take double the above time?
Some explanation for how to calculate that and a breakdown into the time it would take in seconds, minutes, hours, days or years would be much appreciated.