Remember, when "true" quantum computers become a reality, far more than bitcoin is defeated. HTTPS (which uses RSA) is defeated. So basically all internet traffic (passwords, credit card numbers, etc) will be readable by anyone on the same wifi, by an employee at your ISP, or someone at your ISP's ISP, etc.
If I can break ECDSA with a quantum computer I can steal all the money on bitcoin and make all the bitcoins disappear from day to night.
However if i can break RSA, banks and people only have to stop relying on SSL meanwhile they implement a new algorithm. ( Probably they would have to stop using credit cards for a while but they won't loose all their money at all )
So, the first problem is that a quantum computer able to break crypto is a death threat to Bitcoin, meanwhile for a bank that relies on RSA is only a major threat.
The second problem is that the first company who will own a quantum computer able to break crypto will be sure the "US Government". And in the future, when Bitcoin will be much popular than now, I am sure that the US Goverment will have strong incentives to make bitcoin disappear because the bitcoin thing is a major threat to the debt-based economic system of the dollar.
So far.. how much you think will take to the US Gov own such quantum computer and break the ECDSA system of bitcoin? 5 years perhaps?
who cares? (although i'd be more likely to bet on 10+ years...)
in five years Bitcoin will either be worth too much to destroy - and all governments will be in the process of changing their tax-base from income-based to consumption-based...
...or Bitcoin will be worth nothing.