Quantum computation is based on the superposition principle of quantum physics. Bits in a normal computer are either 0 or 1. Quantum physics allows bits to be in a superposition of 0 and 1, in the same way, Schrödinger’s cat can be in a superposition of “alive” and “dead.” [http://nautil.us]
My question is: Can public key cryptography survive quantum computers?
Current commonly used public key cryptography systems are based on the hardness assumption of factorization and/or discrete lograrithm.
Both these problems are solved efficiently using Shor's algorithm using a quantum computer.
Should someone build a quantum computer capable of running the algorithm with thousands of qbits and the ability to apply enough operations on them without decoherence, then it would break RSA and diffie-hellman including elliptic curvre variants.
This breaks all commonly used public key cryptography but does not break all known public key cryptography. There are other asymmetirc algorithms, for example those based on lattice problems which are currently believed to be secure even in the face of quantum computers.
Can public key cryptography survive quantum computers?
Yes.
All current PKC implementations might sooner or later be insecure due to sufficiently powerful quantum computer running Shor's algorithm.
But there already exists an algorithm for post-quantum-PKC: Supersingular isogeny key exchange. This is a likely candidate for post-quantum-PKC, probably this or a smiliar algorithm will be used once powerful quantum computers exist.
