Quantum circulant preconditioner for a linear system of equations
Shao, Changpeng1; Xiang, Hua2
Source PublicationPHYSICAL REVIEW A
AbstractWe 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).
Funding ProjectNatural Science Foundation of China[11571265] ; Natural Science Foundation of China[11471253] ; NSFC-RGC[11661161017] ; NSFC[11671388] ; CAS Project[QYZDJ-SSW-SYS022]
WOS Research AreaOptics ; Physics
WOS SubjectOptics ; Physics, Atomic, Molecular & Chemical
WOS IDWOS:000454150700002
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Document Type期刊论文
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China
Recommended Citation
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.
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