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.
Authors
- Rui‐Chen Huang (ORCID: https://orcid.org/0000-0001-8545-5618)
- Z.P. Zhang
- Guang‐Bao Xu (ORCID: https://orcid.org/0000-0002-9603-0436)
- Yu‐Guang Yang (ORCID: https://orcid.org/0000-0002-4040-2448)
- Zhenwen Cheng
- ZhongXiang Zhang (ORCID: https://orcid.org/0000-0003-3479-8666)
- Shang Gao (ORCID: https://orcid.org/0000-0002-1595-3176)
- Bing‐Xin Liu (ORCID: https://orcid.org/0009-0006-9741-6329)
- Honglin Xie
Institutions
- China Three Gorges Corporation (China) (CN)
- Shandong Normal University (CN)
- Beijing University of Technology (CN)
- Shandong Women’s University (CN)
- Shandong University of Science and Technology (CN)
Publication Details
- Journal
- EPJ Quantum Technology
- Published
- 2025-10-15
- DOI
- https://doi.org/10.1140/epjqt/s40507-025-00423-5
- Primary Topic
- Quantum Computing Algorithms and Architecture
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China
- Natural Science Foundation of Shandong Province