That will hardly be a reasonable concern in the recent future. There are few reasons why. First, quantum computing is still in its early phase and it would take a lot of time until it reaches the level which could harm Bitcoin network.
The other important thing is simply the nature of Bitcoin. It is constantly changing and evolving with mutual consent of its users. So, if quantum computing evolves, so will Bitcoin, and that is something certain. Bitcoin had its difficulties from the beginning until now, and every time Bitcoin network managed to overcome those difficulties.
What is quantum computing? It is an entirely different approach to the computing. Classical computers are like big calculators. Since the technology advanced, people now can create complex engines that could solve some of the math problems far easier and faster. That also includes Bitcoin keys. Those keys are actually addresses that have been used for Bitcoin transactions. In theory, with quantum computing one could break Bitcoin’s “elliptic-curve” cryptography and take advantage of the information gathered, since it is open inside the block.
These concerns came into the focus of the online community since the Microsoft and Google announced that they will create a quantum codes for security of their networks. When it comes to Bitcoin, there are no similar concerns, since only the address that is used for sending or spending Bitcoin has public key. Bitcoin wallets already stopped using already active addresses. This way anyone trying to break Bitcoin security walls with quantum codes will literally find nothing. If one wants to be even more careful, it is enough to simply send all the value from one address at the time. That way even if your privacy is in danger, you will not lose any of your funds.
Besides that, democratic and decentralized network like Bitcoin, already has the capacity to change in order to adjust to the change in technology globally. I strongly believe that in case of quantum computing that will be true again.