In recent years, scientists have some inspiring breakthroughes in quantum algorithm. In 1994, Peter Shor published the Shor's Algorithm. He used the parallel property of quantum computing to do the quantum Fourier transform. In this way, quantum computer can both factor large integers and solve discrete logarithm problems in polynomial time. Shor's Algorithm proved that most of current used public key systems such as RSA and ElGamal will be solved with quantum computers in polynomial time. Therefore, scientists began to research on cryptography which is based on quantum physical qualities. In this paper, we designed two password authentication protocols. The security of the protocols is not based on classical computational complexity but on the principle of quantum mechanics. The first protocol uses additional quantum bits to prevent attackers. In this protocol, the transmitted bits are less than directly using BB84 protocol to generate a key and encode the password. The second protocol uses the property of quantum transmission. We used hash functions to increase the relationship between quantum bits, so the attackers can not get direct information from eavesdropped quantum bits. Our objective is to show that the security of the protocols is not based on the irreversibility of functions, but on the properties of quantum mechanics.