AES works with a shared key. This won’t work when you want to have an encrypted connection with a webshop (how would you get the key over there in a secure way?). For this you have asynchronous key algorithms such as RSA en ECDH. These algorithms can make a secure connection without anything preshared. Usually this is used to compute a shared key and then continue over AES. These asynchronous algorithms are at risk of being cracked with quantum computers.
There’s Grover’s algorithm which can help in cracking the key.
https://crypto.stackexchange.com/questions/6712/is-aes-256-a-post-quantum-secure-cipher-or-not#7869
Regardless, everything sane uses 256 bit AES. Should be ok for now.
AES works with a shared key. This won’t work when you want to have an encrypted connection with a webshop (how would you get the key over there in a secure way?). For this you have asynchronous key algorithms such as RSA en ECDH. These algorithms can make a secure connection without anything preshared. Usually this is used to compute a shared key and then continue over AES. These asynchronous algorithms are at risk of being cracked with quantum computers.