Quantum finite automata: A modern introduction

TL;DR

This paper introduces quantum finite automata (QFAs), demonstrating their advantages over classical automata through examples and presenting a modern superoperator-based model that unifies various automaton types.

Contribution

It provides a modern QFA model capable of simulating all known QFA and classical automaton variants, with practical examples of quantum advantage.

Findings

QFAs outperform classical automata in five example scenarios

A unified superoperator-based QFA model is proposed

The model can simulate all known QFA and classical automata variants

Abstract

We present five examples where quantum finite automata (QFAs) outperform their classical counterparts. This may be useful as a relatively simple technique to introduce quantum computation concepts to computer scientists. We also describe a modern QFA model involving superoperators that is able to simulate all known QFA and classical finite automaton variants.