What effects would a scalable Quantum Computer have on Bitcoin?
You have a good discussion in:

https://bitcointalk.org/index.php?topic=133425.0

Basically, ECDSA is compromised, hashing isn't. With a quantum computer, you could easily deduce the private key corresponding to a public key. If you only have an address, which is a hashed public key, the private key is safe. Anyway, to spend a transaction, you need to send the public key. At that point you are vulnerable, but the attack is not straightforward. 

In general, quantum computers are not exponentially better than classical computers. You cannot access all the states in the superposition, only global properties. You can read http://www.cs.virginia.edu/~robins/The_Limits_of_Quantum_Computers.pdf to get a good idea of what they can and cannot do.