Quantum computers can pwn RSA with Shors algorithm. Quantum computers have already been used for prime factorization just against really small numbers. A quantum computers ability to pwn RSA is dependent on the size of the key versus the number of qubits the quantum computer has. Real cryptographers are worried about quantum computers though, and the number of stabilized qubits is indeed growing at a steady rate. I have heard that RSA with realistic key size is probably going to be dead within a decade or so. Bit for bit ECC is significantly stronger than RSA, although it is still weak to quantum computing attacks, it requires significantly more qubits to pwn ECC based algorithms than RSA, bit to bit. There are public key encryption algorithms that are so far immune to quantum computing, traditionally they have had very large key sizes and very large ciphertexts (measured in megabytes instead of bits) but I believe there are some other quantum resistant techniques that have more practical parameters. Merkle hash tree signatures are quantum resistant, and there are quantum resistant multi-variable quadratic PK crypto schemes for signatures and session key encryption, also goppa code pk schemes that are quantum resistant. NSA currently suggests using elliptic curve PK crypto, they don't even include RSA on their list of suggested algorithms, but it is still thought to be secure against all but quantum computer attacks once you get to ~2,048 bit keys.