Learning Quantum Finite Automata with Queries

TL;DR

This paper introduces polynomial-time algorithms for learning two types of one-way quantum finite automata using query-based methods, advancing quantum model learning in machine learning.

Contribution

It presents the first polynomial-time learning algorithms for measure-once and measure-many one-way QFA with query complexity analysis.

Findings

Polynomial-time learning algorithms for MO-1QFA and MM-1QFA.

Query complexity is polynomial for both models.

Advances quantum automata learning theory.

Abstract

{\it Learning finite automata} (termed as {\it model learning}) has become an important field in machine learning and has been useful realistic applications. Quantum finite automata (QFA) are simple models of quantum computers with finite memory. Due to their simplicity, QFA have well physical realizability, but one-way QFA still have essential advantages over classical finite automata with regard to state complexity (two-way QFA are more powerful than classical finite automata in computation ability as well). As a different problem in {\it quantum learning theory} and {\it quantum machine learning}, in this paper, our purpose is to initiate the study of {\it learning QFA with queries} (naturally it may be termed as {\it quantum model learning}), and the main results are regarding learning two basic one-way QFA: (1) We propose a learning algorithm for measure-once one-way QFA (MO-1QFA) with query complexity of polynomial time; (2) We propose a learning algorithm for measure-many one-way QFA (MM-1QFA) with query complexity of polynomial-time, as well.