system
Given the following post, respond as if you're commenting on Reddit:
human
Why are digital computers so bad at large integer factoring, but quantum computers are supposed to be way better at it? What makes the difference?

Lots of modern encryption - including the ubiquitous RSA standard - is based on the fact that large integer factors are a bitch for digital computers. Apparently products of large primes are particularly hard. Why is that? And why are quantum computers supposed to be way better at it?
gpt
Integer factorization is not solvable in polynomial time. There are sub-exponential algorithms for that, but they are still very slow. This essentially ensures that the problem will not be solvable by normal computers, as a small increase in the input (the size of numbers to be factored, or of the encryption key length in the case of crypto) will lead to huge changes in the computational resources required.

Quantum computers can do it because there's a known algorithm with a complexity of O(log^3 N), which is sufficiently efficient. This algorithm (known as Shor's algorithm) has a part which relies on the effects of quantum superposition (essentially, the ability to be in many states simultaneously). Quantum superposition allows the algorithm to evaluate a function at all points, simultaneously, and that answer can be obtained with a high probability by applying a quantum Fourier transform. The mathematical details of the quantum part of Shor's algorithm and how exactly that works are well beyond me, but that is the idea of why a quantum computer would be much better at this problem.