DOI: 10.1016/j.scib.2021.06.023
论文题名: Variational algorithms for linear algebra
作者: Xu X. ; Sun J. ; Endo S. ; Li Y. ; Benjamin S.C. ; Yuan X.
刊名: Science Bulletin
ISSN: 20959273
出版年: 2021
语种: 英语
中文关键词: Linear algebra
; Matrix multiplication
; Quantum computing
; Quantum simulation
; Variational quantum eigensolver
英文摘要: Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices. We show that the solutions of linear systems of equations and matrix–vector multiplications can be translated as the ground states of the constructed Hamiltonians. Based on the variational quantum algorithms, we introduce Hamiltonian morphing together with an adaptive ansätz for efficiently finding the ground state, and show the solution verification. Our algorithms are especially suitable for linear algebra problems with sparse matrices, and have wide applications in machine learning and optimisation problems. The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation. We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations. We implement the algorithm on the IBM Q device with a high solution fidelity of 99.95%. © 2021 Science China Press Citation statistics:
资源类型: 期刊论文
标识符: http://119.78.100.158/handle/2HF3EXSE/170467
Appears in Collections: 气候变化与战略
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作者单位: Center on Frontiers of Computing Studies, Department of Computer Science, Peking University, Beijing, 100871, China; Department of Materials, University of Oxford, Oxford, OX1 3PH, United Kingdom; Clarendon Laboratory, University of Oxford, Oxford, OX1 3PU, United Kingdom; Graduate School of China Academy of Engineering Physics, Beijing, 100193, China
Recommended Citation:
Xu X.,Sun J.,Endo S.,et al. Variational algorithms for linear algebra[J]. Science Bulletin,2021-01-01