It's worth pointing out that other public-key encryption algorithms don't have the same vulnerability to quantum computers. It's also unlikely (but unproven) that quantum computers can solve NP-complete problems.
PGP is a piece of software, and not an algorithm. I believe it uses RSA and AES by default, but I could be wrong :)
AFAIK RSA, DSA, Diffie-Hellman, and ECC are all known to be vulnerable to Shor's Algorithm (which, granted, do make up a lot of the crypto in common use), but there are lesser-used algorithms like McEliece and NTRU that are not vulnerable.
That said, quantum computers are still very far from breaking modern cryptography. We're playing around with a handful of qubits, but to break something like a 4096 bit RSA key would take trillions of quantum gates.