They say that public key infrastructure or PKI uses very complex encryption. What if that encryption breaks one day when quantum computers complete? What if they decrypt all private messages and data? What will be the replacement then?
Quantum computing is being developed to attack specific algorithms. Right now there are efforts under way to find algorithms that are resistant to quantum computing attacks. Such algorithms are called post-quantum.
The Public Key Infrastructure is built on the concept of certificates, not algorithms. Certificates are documents that are capable of storing many types of signatures using many different algorithms. If one algorithm falls, such as happened when MD5 was found to have weaknesses allowing the forging of certificates, we can stop using it and switch to another.
Researchers give us warnings as they close in on weaknesses. An example of this happened a couple of years ago when SHA-1 fell to an attack. Even though there was no immediately apparent vulnerability to certificates, people stopped trusting SHA-1 signatures on certificates, and switched to alternatives.
As quantum computing approaches the capability of cracking a specific algorithm such as RSA, the world will switch certificates to trusting only post-quantum algorithms. PKIs will continue.
Throughout history, cryptography has always been a game of cat and mouse. The ability to modify keys, algorithms, and protocols has always been critical to maintaining security. Quantum computing may be a threat, but not necessarily a game ender.