Quantum Hashing via Classical $\epsilon$-universal Hashing Constructions
  In the paper, we define the concept of the quantum hash generator and offer design, which allows to build a large amount of different quantum hash functions. The construction is based on composition of classical $\epsilon$-universal hash family and a given family of functions -- quantum hash generator.   The proposed construction combines the properties of robust presentation of information by classical error-correcting codes together with the possibility of highly compressed presentation of information by quantum systems.   In particularly, we present quantum hash function based on Reed-Solomon code, and we proved, that this construction is optimal in the sense of number of qubits needed. 
Farid Ablayev, Marat Ablayev
quant-ph cs.CR