What is Quantum-Resistant or Post-Quantum Cryptography

Apr 2016 National Institute of Standards and Technology published Report on Post-Quantum Cryptography basically confirming “If large-scale quantum computers are ever built, they will be able to break many of the public-key cryptosystems currently in use” (https://csrc.nist.gov/publications/detail/nistir/8105/final). We are not at 50-qubit computers already build with 70+ qubits in research or to be released in 2018/19. It was claimed that once 100-qubits limit is surpassed — any size of quantum computer to be build.