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DOI	10.1016/j.scib.2021.06.023
	Variational algorithms for linear algebra
	Xu X.; Sun J.; Endo S.; Li Y.; Benjamin S.C.; Yuan X.
发表日期	2021
ISSN	20959273
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
关键词	Linear algebra Matrix multiplication Quantum computing Quantum simulation Variational quantum eigensolver
语种	英语
来源期刊	Science Bulletin
文献类型	期刊论文
条目标识符	http://gcip.llas.ac.cn/handle/2XKMVOVA/207633
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
推荐引用方式 GB/T 7714	Xu X.,Sun J.,Endo S.,et al. Variational algorithms for linear algebra[J],2021.
APA	Xu X.,Sun J.,Endo S.,Li Y.,Benjamin S.C.,&Yuan X..(2021).Variational algorithms for linear algebra.Science Bulletin.
MLA	Xu X.,et al."Variational algorithms for linear algebra".Science Bulletin (2021).