The cryptography community has already started preparation for the post-quantum world. For example, there is a paper by Daniel J. Bernstein (et al.) ''Post-quantum RSA'' (https://cr.yp.to/papers/pqrsa-20170419.pdf), where authors propose RSA parameters for which:

Based on that I assume that a lot of traditional protocols will be adjusted to the modifications of classical DH and RSA. On the other hand, alternative public key algorithms attract increasing attention, e.g. hash-based cryptography, code-based cryptography or lattice-based cryptography. Thus, protocols based on those concepts will become an interesting alternative.

Dear Tomasz Mazurkiewicz, firstly, thank for your answer.

Since the IoT devices have constraints in its memory, computation and packet size, the post-quantum cryptography needs a larger key size and more consume computation than traditional cryptography. Therefore, it may not suitable for IoT devices.

Dear Zeyad,

To achieve efficient leveled authentication I would recommend lightweight Lattice Encryption.

I recommended lightweight lattice and isogeny of elliptic curves for securing IoT, Edge and Fog computing.

Thank to Tomasz Mazurkiewicz and Aws Naser Jaber for answering the question