When quantum computers start breaking classic cryptography, then we better already have something stronger at hand - like quantum cryptography. The good news is that quantum cryptography is more simple than quantum computing.

Quantum Cryptography Protocols

For starters there are the quantum crypto protocols BB84 and E91.

BB84Charles Bennet and Gilles BrassardPolarized Photons
E91Artur EkertEntangled Photon Pairs

On BB84 I wrote a seminar report in the course of my Bachelor studies.