On hybrid models of quantum finite automata

TL;DR

This paper introduces a comprehensive hybrid quantum-classical finite automata model, unifying existing models and clarifying their relationships with other quantum automata, highlighting their advantages over fully quantum models.

Contribution

It proposes a general hybrid model of quantum finite automata with interaction between quantum and classical parts, unifying and analyzing existing models within this framework.

Findings

Hybrid QFA can be exactly simulated by QFA with quantum operations.

Existing hybrid models correspond to specific communication patterns.

Hybrid QFA relate closely to ancilla QFA and quantum sequential machines.

Abstract

In the literature, there exist several quantum finite automata (QFA) models with both quantum and classical states. These models are of particular interest,as they show praiseworthy advantages over the fully quantum models in some nontrivial aspects. This paper characterizes these models in a uniform framework by proposing a general hybrid model consisting of a quantum component and a classical one which can interact with each other. The existing hybrid QFA can be naturally regarded as the general model with specific communication patterns (classical-quantum, quantum-classical, and two-way, respectively). We further clarify the relationship between these hybrid QFA and some other quantum models. In particular, it is shown that hybrid QFA can be simulated exactly by QFA with quantum operations, which in turn has a close relationship with two early proposed models: {\it ancialla QFA} and {\it quantum sequential machines}.