What is the simplest post-quantum asymmetric cryptographic algorithm for key exchange?
There is only one paper I know of which explains a post-quantum key exchange algorithm in such a way that a beginner could understand it, and that is for SIDH (Supersingular Isogeny Diffie-Hellman key exchange). The paper is called Supersingular isogeny key exchange for beginners.

Abstract. This is an informal tutorial on the supersingular isogeny Diffie-Hellman protocol aimed at non-isogenists.

If you don't care whether or not it is actually usable, then there's pqRSA which is essentially just regular RSA with (completely impractical) parameters that make it post-quantum secure.