Quantum multirow iteration algorithm for linear systems with nonsquare coefficient matrices
文献类型：期刊论文
| 作者 | Lin, Weitao1; Tian, Guojing1; Sun, Xiaoming1 |
| 刊名 | PHYSICAL REVIEW A
 |
| 出版日期 | 2024-08-27 |
| 卷号 | 110期号:2页码:14 |
| ISSN号 | 2469-9926 |
| DOI | 10.1103/PhysRevA.110.022438 |
| 英文摘要 | In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms addressing nonsquare matrices. Towards this kind of problems defined by Ax = b where A E Rm`n, we propose a quantum algorithm inspired by the classical multirow iteration method and provide an explicit quantum circuit based on the quantum comparator and quantum random access memory. The time complexity of our quantum multirow iteration algorithm is O(K log2 m), with K representing the number of iteration steps, which demonstrates an exponential speedup compared to the classical version.. Based on the convergence of the classical multirow iteration algorithm, we prove that our quantum algorithm converges faster than the quantum one-row iteration algorithm presented by Shao and Xiang [C. Shao and H. Xiang, Phys. Rev. A 101, 022322 (2020)]. Moreover, our algorithm places less demand on the coefficient matrix, making it suitable for solving inconsistent systems and quadratic optimization problems. |
| 资助项目 | National Natural Science Foundation of China[62325210] ; National Natural Science Foundation of China[62272441] ; National Natural Science Foundation of China[12204489] ; National Natural Science Foundation of China[62301531] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDB28000000] |
| WOS研究方向 | Optics ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:001302457900004 |
| 出版者 | AMER PHYSICAL SOC |
| 源URL | [http://119.78.100.204/handle/2XEOYT63/39493]  |
| 专题 | 中国科学院计算技术研究所期刊论文_英文 |
| 通讯作者 | Lin, Weitao |
| 作者单位 | 1.Chinese Acad Sci, Inst Comp Technol, State Key Lab Processors, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China |
| 推荐引用方式 GB/T 7714 | Lin, Weitao,Tian, Guojing,Sun, Xiaoming. Quantum multirow iteration algorithm for linear systems with nonsquare coefficient matrices[J]. PHYSICAL REVIEW A,2024,110(2):14. |
| APA | Lin, Weitao,Tian, Guojing,&Sun, Xiaoming.(2024).Quantum multirow iteration algorithm for linear systems with nonsquare coefficient matrices.PHYSICAL REVIEW A,110(2),14. |
| MLA | Lin, Weitao,et al."Quantum multirow iteration algorithm for linear systems with nonsquare coefficient matrices".PHYSICAL REVIEW A 110.2(2024):14. |
入库方式： OAI收割
来源：计算技术研究所
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