Nope. Quantum computers will not exist that can break Bitcoin's cryptography for at least 10-20 years, and when they do, the solution is very easy.
Once quantum computers are advanced enough, the public key algorithm can be changed via a soft fork. People would have to move their coins to addresses using the new algorithm in order to secure them.
Bitcoin is not the only thing that will be affected by this. Many other systems will also need to be updated.
Yes its said that work is already going on to avoid such attacks by quantum computers in the future and it would take atleast 20 more years for quantum computers to come in to existence.Its said that quantum computers would have the ability to read the private key of a wallet from its public key itself.
