Using Qubits doesn't automatically make everything faster. There are certain quantum algorithms that can only be run on quantum computers that take advantage of qubits. These algorithm's might be able to solve certain problems "faster" but not necessarily in linear terms -- that is, you wouldn't be able to say it did something ten, or one hundred, or one million times faster, it's more like a "did you get an answer or not?" type of situation.
Another important question might be, Can the bitcoin mining algorithm be converted into such a quantum algorithm?.
I don't know if there is an answer for that, but if we can find such an algorithm, this could theoretically break bitcoin.
Sounds absurd, yes, but consider this -- the difficulty for the entire network is based on how fast blocks are found -- if blocks are found faster than normal, the network permanently increases the difficulty to compensate.
A quantum computer would be able to mine a block pretty much instantly and if introduced into the network, it would cause the difficulty to skyrocket, effectively locking out all other computers on the network from being able to mine simply because it's hard for them.
You might want be tempted to simply build the same network just using quantum computers entirely, but if the aforementioned difficulty reaches the maximum difficulty as defined by the protocol, all quantum computers on the network would mine blocks instantaneously, immediately forking the block-chain at every node. In order to fix this, the entire protocol would have to change in order to avoid any pitfalls brought about by quantum computing.
While technically a separate entity from the bitcoin system, it should be noted that the address system is also potentially vulnerable. Algorithms exist that, if run on a quantum computer, can find a private key that matches a given public address. While the mining may or may not be effected by quantum algorithms, the security definitely is.
So, to answer your question explicitly -- maybe, and if so, it would destroy the mining community.
But let's not forget, that this is all still speculation. It might not be possible to modify the mining algorithm to run on top of qubits. Even if it is possible, it is still debatable as to whether or not a true quantum computer can be built.