Superiority of one-way and realtime quantum machines and new directions

TL;DR

This paper explores the enhanced computational power of one-way and realtime quantum automata, including new models with multiple input heads, demonstrating their advantages over classical automata and proposing future research directions.

Contribution

It introduces novel quantum automata models with multiple input heads and analyzes their superiority over classical automata, along with proposing open problems and new classical results.

Findings

Quantum automata with multiple input heads outperform classical counterparts.

One-way and realtime quantum automata show significant advantages.

New results on classical computation are also presented.

Abstract

In automata theory, the quantum computation has been widely examined for finite state machines, known as quantum finite automata (QFAs), and less attention has been given to the QFAs augmented with counters or stacks. Moreover, to our knowledge, there is no result related to QFAs having more than one input head. In this paper, we focus on such generalizations of QFAs whose input head(s) operate(s) in one-way or realtime mode and present many superiority of them to their classical counterparts. Furthermore, we propose some open problems and conjectures in order to investigate the power of quantumness better. We also give some new results on classical computation.