If quantum computer becomes a reality, then certainly it will pose a real threat to bitcoin security. I had read a report by MIT on this actual subject few months back. They said the threat is real and imminent but it would take more than a decade before we can see it actually happening.
You can read it from the below link,
https://www.technologyreview.com/s/609408/quantum-computers-pose-imminent-threat-to-bitcoin-security/However, I can tell you two reasons why you should not worry.
Firstly, quantum computer doesn't exist in perfect world, except in theories! It is being developed and we still don't know anything of its progresses. It may take 3 years, it may take 5 years or even more! It may not even become a reality!
Secondly, quantum computers is being developed for specialized purposes and it will not be available in the market for anyone to buy and use, at least for next 2 - 3 decades! So it is highly unlikely to be misused for any other puspose. Unless a particular government wants to use quantum computer for destroying cryptocurrency, your bitcoins are very much safe!
Technologies will be evolved and become more powerful. That is the nature of technology. Who knows, by then probably we will have new security protocols available to prevent any breach by the quantum computers!
