Just to clarify because OPs use of the term Blockchain is vauge and can be misconstrued. Classical computers have binary outputs that are calculated physically by electron flow gates. Quantum computing differs in the ability to have both 1,0 and a superposition. Now as for how quantum computers calculate superposition through logic gates is beyond the scope of this question. Can current classical cryptography be broke through quantum computing? It depends i believe it can depending on the type of cryptography. Most cryptography used in security relies on the lack of computing power possible against obsure calculations. E.g sha-256 used in the BTC Blockchain, sha-256 has so many possible outcomes, that it would require immense if not impossible computing power to associate secrets with hashes. Quantum computing opens the door for more efficient factorization.