Quantum hashing. Group approach

TL;DR

This paper generalizes quantum hash functions to arbitrary groups, demonstrating their existence for abelian groups, constructing key automorphisms, and analyzing limitations on Hilbert space and group choices.

Contribution

It introduces a framework for quantum hash functions on arbitrary groups and constructs automorphisms, expanding the theoretical foundation of quantum hashing.

Findings

Quantum hash functions exist for all abelian groups.

Constructed a set of 'good' automorphisms for quantum hash functions.

Identified restrictions on Hilbert space dimension and group selection.

Abstract

In this paper we consider a generalization of quantum hash functions for arbitrary groups. We show that quantum hash function exists for arbitrary abelian group. We construct a set of "good" automorphisms --- a key component of quantum hash funciton. We prove some restrictions on Hilbert space dimension and group used in quantum hash function