Quantum circulant preconditioner for a linear system of equations

doi:10.1103/PhysRevA.98.062321

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	Quantum circulant preconditioner for a linear system of equations
	Shao, Changpeng 1; Xiang, Hua 2
	2018-12-18
发表期刊	PHYSICAL REVIEW A
ISSN	2469-9926
卷号	98 期号:6 页码:9
摘要	We consider the quantum linear solver for Ax = b with the circulant preconditioner C. The main technique is the singular value estimation (SVE) introduced in [Kerenidis and Prakash, Quantum recommendation system, in ITCS (2017)]. However, the SVE should be modified to solve the preconditioned linear system C(-1)Ax = C(-1)b. Moreover, different from the preconditioned linear system considered in [Phys. Rev. Lett. 110, 250504 (2013)], the circulant preconditioner is easy to construct and can be directly applied to general dense non-Hermitian cases. The time complexity depends on the condition numbers of C and C-1 A, as well as the Frobenius norm parallel to A parallel to(F).
DOI	10.1103/PhysRevA.98.062321
语种	英语
资助项目	Natural Science Foundation of China[11571265] ; Natural Science Foundation of China[11471253] ; NSFC-RGC[11661161017] ; NSFC[11671388] ; CAS Project[QYZDJ-SSW-SYS022]
WOS研究方向	Optics ; Physics
WOS类目	Optics ; Physics, Atomic, Molecular & Chemical
WOS记录号	WOS:000454150700002
出版者	AMER PHYSICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31912
专题	中国科学院数学与系统科学研究院
通讯作者	Xiang, Hua
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China
推荐引用方式 GB/T 7714	Shao, Changpeng,Xiang, Hua. Quantum circulant preconditioner for a linear system of equations[J]. PHYSICAL REVIEW A,2018,98(6):9.
APA	Shao, Changpeng,&Xiang, Hua.(2018).Quantum circulant preconditioner for a linear system of equations.PHYSICAL REVIEW A,98(6),9.
MLA	Shao, Changpeng,et al."Quantum circulant preconditioner for a linear system of equations".PHYSICAL REVIEW A 98.6(2018):9.