The specific types of mathematical calculations being done by a miner is referred to as the hashing algorithm of the network. Quai Network utilizes the ProgPoW hashing algorithm, an evolution of Ethash designed for improved ASIC resistance.

The ProgPoW algorithm was chosen due to the difficulty of creating application-specific integrated circuits (ASICs) that can mine ProgPoW. The use of ASIC-able algorithms such as SHA-256 quickly renders consumer-grade hardware impractical, resulting in large barrier to entry for competitive mining.

ProgPoW was developed as an EIP to replace Ethash, but was discarded due to the merge. The original ProgPoW EIP (EIP-1057) can be found here. Additional information on ProgPoW can be found on the ETH Magicians forum here.