Post-quantum hybrid encryption Assume the following simplified protocol:


seed = curve25519SharedKey(theirPublicKey, myPrivateKey)
sharedKey = scrypt(seed, salt, sufficientlyHardWorkFactors...)
cipherText = aes256(sharedKey, clearText)


Does using a slow-hash on the output of an asymmetric key-exchange offer any more protection in a quantum-computing era?  I know that quantum computing is supposed to make breaking diffie-hellman easy... what I don't know is exactly how easy.  Is the algorithm (greatly) diminished, or completely broken?
Does using a slow-hash on the output of an asymmetric key-exchange
  
  offer any more protection in a quantum-computing era?


No. $\:$ A quantum attacker would simply find seed even if you didn't use "a slow-hash on" it.



  Is the algorithm (greatly) diminished, or completely broken?


The algorithm will still be completely broken by quantum attacks. $\:$ Furthermore, your simplified

protocol would just have one more link (scrypt) that could potentially be broken by classical attacks.