Post-quantum cryptography encompasses the algorithms that are allegedly immune against quantum computing. There are five categories that seem suitable for post-quantum cryptography. See previous post.
In 2017, NIST initiated the process to select and standardize a set of post-quantum cryptosystems. In 2019, the second round selected 26 candidates. The third round started in 2020. Last month, NIST published an intermediary analysis of these candidates. As a result, NIST selected seven serious candidates and eight potential but unlikely contenders. The draft standards should be available by 2024. Table 1 lists the nine candidates for encryption. The predominance of lattice-based and code-based solutions is visible. Table 2 lists the six selected candidates for digital signatures. The more likely candidates are highlighted.

Lattice seems to be the big runner for post-quantum. A future post will attempt to give a hint on lattice-based cryptography.

The report is available at https://nvlpubs.nist.gov/nistpubs/ir/2020/NIST.IR.8309.pdf