用查询学习量子有限自动机

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS Mathematical Structures in Computer Science Pub Date : 2023-11-30 DOI:10.1017/s0960129523000373
Daowen Qiu
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引用次数: 0

摘要

有限自动机学习(也称为模型学习)已成为机器学习的一个重要领域,并在现实中得到了广泛的应用。量子有限自动机(QFA)是具有有限内存的量子计算机的简单模型。由于其简单性,QFA具有良好的物理可实现性,但单向QFA在状态复杂性方面仍比经典有限自动机具有本质优势(双向QFA在计算能力方面也比经典有限自动机更强大)。作为量子学习理论和量子机器学习中的一个不同的问题,在本文中,我们的目的是启动使用查询学习QFA的研究(自然它可以被称为量子模型学习),主要结果是关于学习两个基本的单向QFA (1QFA):(1)提出了一种查询复杂度为多项式时间的测度一次1QFA (MO-1QFA)学习算法;(2)提出了查询复杂度为多项式时间的测度多1QFA (MM-1QFA)学习算法。
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Learning quantum finite automata with queries
Learning finite automata (termed as 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 quantum learning theory and quantum machine learning, in this paper, our purpose is to initiate the study of learning QFA with queries (naturally it may be termed as quantum model learning), and the main results are regarding learning two basic one-way QFA (1QFA): (1) we propose a learning algorithm for measure-once 1QFA (MO-1QFA) with query complexity of polynomial time and (2) we propose a learning algorithm for measure-many 1QFA (MM-1QFA) with query complexity of polynomial time, as well.
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来源期刊
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science 工程技术-计算机:理论方法
CiteScore
1.50
自引率
0.00%
发文量
30
审稿时长
12 months
期刊介绍: Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.
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