Efficient Branching Programs for Quantum Hash Functions Generated by Small-Biased Sets

Abstract

In the paper we consider quantum (δ, ϵ)-hash functions in so called phase form (phase quantum (δ, ϵ)-hash function). It is known that ϵ-biased sets generate phase quantum (δ, ϵ)- hash function. We show that the construction is invertible, that is, phase quantum (δ, ϵ)-hash function defines ϵ-biased sets. Next, we present an efficient (in the sense of time and qubits needed) Branching program construction for phase quantum (δ, ϵ)-hash function.