Highly unlikely at least for a while. Its been discussed so many times its almost becoming tedious. Quantum computers which are actually designed to break algorithms don't only apply to Bitcoin, but apply to everything that implements those algorithms. That's including banks, Google, and whatever else you can think of. However, quantum computers aren't particularly good at everything, they are designed to be good at one thing in particular. Therefore, to own a quantum computer which needs to be stationed in a controlled environment isn't likely going to fall into the hands of criminals, unless of course you consider the government to be criminals.

The government, military, and potentially high profile companies are the only ones that would be able to afford quantum computers, and even then a smaller division of this number will actually have a need for quantum computers. I would say that the government, and military are the only ones which could justify the cost. Now, you could say that the government are hostile towards Bitcoin, but that entirely depends on the government your talking about. Many governments have actually successfully regulated Bitcoin, and therefore Bitcoin earns them more money than not having it. By breaking Bitcoin if that was even theoretically possible would actually reduce the amount of money they earn. Bitcoin, isn't likely to replace fiat currencies, at least not for a long time. In fact, Bitcoin is probably not something that would replace it, but a similar implementation of Bitcoin might. Therefore, Bitcoin in its current state is of limited threat, and actually benefits the governments that have successfully regulated it.

By the time, Bitcoin was to become a threat or quantum computers became affordable enough to own for others, Bitcoin as well as banks, and other big industries would have already implemented quantum resistant algorithms, effectively making it redundant.

Quantum computers aren't even particularly good for hacking, they are good at breaking a specific type of algorithm, and wouldn't be able to be used for anything other than that. The biggest benefit of a quantum computer is using it in the military for obvious reasons.