多项式乘法的量子算法及其应用

IF 5.6 2区物理与天体物理 Q1 OPTICS

EPJ Quantum Technology Pub Date : 2025-10-15 DOI:10.1140/epjqt/s40507-025-00423-5

Shang Gao, Rui-Chen Huang, Bing-Xin Liu, Zhen-Wen Cheng, Hong-Lin Xie, Zhong-Xiang Zhang, Zhao-Qian Zhang, Guang-Bao Xu, Yu-Guang Yang

{"title":"多项式乘法的量子算法及其应用","authors":"Shang Gao, Rui-Chen Huang, Bing-Xin Liu, Zhen-Wen Cheng, Hong-Lin Xie, Zhong-Xiang Zhang, Zhao-Qian Zhang, Guang-Bao Xu, Yu-Guang Yang","doi":"10.1140/epjqt/s40507-025-00423-5","DOIUrl":null,"url":null,"abstract":"<div><p>Polynomial multiplication is a fundamental operation in various fields of science and engineering. This paper proposes a quantum algorithm for polynomial multiplication that achieves improved efficiency over classical approaches. The core innovation is the use of a quantum Fourier transform with digital encoding. The practical utility and versatility of this algorithm are highlighted through its application to several related computational problems, including string matching, Toeplitz matrix-vector multiplication, and matrix decomposition algorithm. Furthermore, an enhanced version of the quantum polynomial multiplication algorithm is introduced, offering improvements in both execution process and time complexity.</p></div>","PeriodicalId":547,"journal":{"name":"EPJ Quantum Technology","volume":"12 1","pages":""},"PeriodicalIF":5.6000,"publicationDate":"2025-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://epjquantumtechnology.springeropen.com/counter/pdf/10.1140/epjqt/s40507-025-00423-5","citationCount":"0","resultStr":"{\"title\":\"Quantum algorithm for polynomial multiplication and its applications\",\"authors\":\"Shang Gao, Rui-Chen Huang, Bing-Xin Liu, Zhen-Wen Cheng, Hong-Lin Xie, Zhong-Xiang Zhang, Zhao-Qian Zhang, Guang-Bao Xu, Yu-Guang Yang\",\"doi\":\"10.1140/epjqt/s40507-025-00423-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Polynomial multiplication is a fundamental operation in various fields of science and engineering. This paper proposes a quantum algorithm for polynomial multiplication that achieves improved efficiency over classical approaches. The core innovation is the use of a quantum Fourier transform with digital encoding. The practical utility and versatility of this algorithm are highlighted through its application to several related computational problems, including string matching, Toeplitz matrix-vector multiplication, and matrix decomposition algorithm. Furthermore, an enhanced version of the quantum polynomial multiplication algorithm is introduced, offering improvements in both execution process and time complexity.</p></div>\",\"PeriodicalId\":547,\"journal\":{\"name\":\"EPJ Quantum Technology\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":5.6000,\"publicationDate\":\"2025-10-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://epjquantumtechnology.springeropen.com/counter/pdf/10.1140/epjqt/s40507-025-00423-5\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"EPJ Quantum Technology\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1140/epjqt/s40507-025-00423-5\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"OPTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPJ Quantum Technology","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1140/epjqt/s40507-025-00423-5","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPTICS","Score":null,"Total":0}

引用次数: 0

摘要

多项式乘法是科学和工程各个领域的基本运算。本文提出了一种多项式乘法的量子算法，该算法比经典方法效率更高。其核心创新是使用带有数字编码的量子傅立叶变换。通过将该算法应用于几个相关的计算问题，包括字符串匹配、Toeplitz矩阵-向量乘法和矩阵分解算法，突出了该算法的实用性和通用性。此外，还介绍了量子多项式乘法算法的增强版本，在执行过程和时间复杂度方面都有改进。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Quantum algorithm for polynomial multiplication and its applications

Polynomial multiplication is a fundamental operation in various fields of science and engineering. This paper proposes a quantum algorithm for polynomial multiplication that achieves improved efficiency over classical approaches. The core innovation is the use of a quantum Fourier transform with digital encoding. The practical utility and versatility of this algorithm are highlighted through its application to several related computational problems, including string matching, Toeplitz matrix-vector multiplication, and matrix decomposition algorithm. Furthermore, an enhanced version of the quantum polynomial multiplication algorithm is introduced, offering improvements in both execution process and time complexity.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

EPJ Quantum Technology Physics and Astronomy-Atomic and Molecular Physics, and Optics

CiteScore

7.70

自引率

7.50%

发文量

审稿时长

71 days

期刊介绍： Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics. EPJ Quantum Technology covers theoretical and experimental advances in subjects including but not limited to the following: Quantum measurement, metrology and lithography Quantum complex systems, networks and cellular automata Quantum electromechanical systems Quantum optomechanical systems Quantum machines, engineering and nanorobotics Quantum control theory Quantum information, communication and computation Quantum thermodynamics Quantum metamaterials The effect of Casimir forces on micro- and nano-electromechanical systems Quantum biology Quantum sensing Hybrid quantum systems Quantum simulations.