If you're not careful with your keys & spending, it might be (Since the private key could be cracked if the attacker has your public key, right(?)), but then again, when the time of quantum computing is here we might have already implemented some kind of "resistance" against it.
See the answer below, and the SE link for some more discussion & useful answers from people that are much more knowledgeable than me on the topic.
You have a good discussion in:
https://bitcointalk.org/index.php?topic=133425.0Basically, 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.
And, as mentioned in the quote above,
https://bitcointalk.org/index.php?topic=133425.0 is pretty informative about the topic as well.
