| 题名 | Quantum algorithms for the generalized eigenvalue problem |
| 作者 | |
| 通讯作者 | Liang，Jin Min |
| 发表日期 | 2022
|
| DOI | |
| 发表期刊 | |
| ISSN | 1570-0755
|
| EISSN | 1573-1332
|
| 卷号 | 21期号:1 |
| 摘要 | The generalized eigenvalue (GE) problems are of particular importance in various areas of science engineering and machine learning. We present a variational quantum algorithm for finding the desired generalized eigenvalue of the GE problem, A| ψ⟩ = λB| ψ⟩ , by choosing suitable loss functions. Our approach imposes the superposition of the trial state and the obtained eigenvectors with respect to the weighting matrix B on the Rayleigh quotient. Furthermore, both the values and derivatives of the loss functions can be calculated on near-term quantum devices with shallow quantum circuit. Finally, we propose a full quantum generalized eigensolver (FQGE) to calculate the minimal generalized eigenvalue with quantum gradient descent algorithm. As a demonstration of the principle, we numerically implement our algorithms to conduct a 2-qubit simulation and successfully find the generalized eigenvalues of the matrix pencil (A,B). The numerically experimental result indicates that FQGE is robust under Gaussian noise. |
| 相关链接 | [Scopus记录] |
| 收录类别 | |
| 语种 | 英语
|
| 学校署名 | 其他
|
| EI入藏号 | 20215211406704
|
| EI主题词 | Eigenvalues and eigenfunctions
; Gaussian noise (electronic)
; Gradient methods
|
| EI分类号 | Numerical Methods:921.6
; Quantum Theory; Quantum Mechanics:931.4
|
| Scopus记录号 | 2-s2.0-85121806144
|
| 来源库 | Scopus
|
| 引用统计 |
被引频次[WOS]：10
|
| 成果类型 | 期刊论文 |
| 条目标识符 | http://sustech.caswiz.com/handle/2SGJ60CL/259929 |
| 专题 | 量子科学与工程研究院 理学院_物理系 |
| 作者单位 | 1.School of Mathematical Science,Capital Normal University,Beijing,10048,China 2.College of Science,China University of Petroleum,Qingdao,266580,China 3.Shenzhen Institute for Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen,518055,China |
| 推荐引用方式 GB/T 7714 |
Liang，Jin Min,Shen，Shu Qian,Li，Ming,et al. Quantum algorithms for the generalized eigenvalue problem[J]. Quantum Information Processing,2022,21(1).
|
| APA |
Liang，Jin Min,Shen，Shu Qian,Li，Ming,&Fei，Shao Ming.(2022).Quantum algorithms for the generalized eigenvalue problem.Quantum Information Processing,21(1).
|
| MLA |
Liang，Jin Min,et al."Quantum algorithms for the generalized eigenvalue problem".Quantum Information Processing 21.1(2022).
|
| 条目包含的文件 | ||||||
| 文件名称/大小 | 文献类型 | 版本类型 | 开放类型 | 使用许可 | 操作 | |
| 10.1007@s11128-021-0（623KB） | -- | -- | 开放获取 | -- | 浏览 | |
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