The cryptographic hardness ultimately relies on something called the discrete logarithm problem over you know finite rebellion groups. Under suitable settings classical algorithms are believed not to be able to do this so quantum computers can efficiently break such systems like RSA defeat helman key exchange elliptic curve cryptography. The snarks used by zcash as well as other recent suggestions such as the beautiful bulletproofs as your knowledge system rely on such hardness assumptions and they are known to be attackable by quantum computers.