I don't know of any research into this area, but it's conceivable that you could have an encryption algorithm that is polynomial time (given the key!) on a quan

I don't know of any research into this area, but it's conceivable that you could have an encryption algorithm that is polynomial time (given the key!) on a quantum computer but exponential time classically, and that has some better security guarantees given certain common assumptions. However, quantum algorithms of any sort are difficult enough to invent that we'll likely end up using classical algorithms that 'look' hard to break with quantum computers, i.e. ones where prime factoring doesn't help. The real quantum defence appears to be something rather different. Quantum cryptography (https://en.wikipedia.org/wiki/Quantum_cryptography https://en.wikipedia.org/wiki/Quantum_cryptography) uses polarised photons to create very strong guarantees that your communication is secure. We can say that if you do the engineering correctly, the laws of physics would have to be violated to intercept your messages.