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Quantum QR decomposition in the computational basis
Ma, Guangsheng1; Li, Hongbo2; Zhao, Jiman1
2020-07-29
Source PublicationQUANTUM INFORMATION PROCESSING
ISSN1570-0755
Volume19Issue:8Pages:16
AbstractIn this paper, we propose a quantum algorithm for approximating the QR decomposition of any N x N matrix with a running time O(1/epsilon(2) N(2.5)polylog( N)), where epsilon is the desired precision. This quantum algorithm provides a polynomial speedup over the best classical algorithm, which has a running time O(N-3). Our quantum algorithm utilizes the quantum computation in the computational basis (QCCB) and a setting of updatable quantum memory. We further present a systematic approach to applying the QCCB to simulate any quantum algorithm. By this approach, the simulation time does not exceed O(N(2)polylog( N)) times the running time of the quantum algorithm originally designed with the amplitude encoding method, where N is the size of the problem.
KeywordQuantum algorithms Computational basis Quantum QR decomposition
DOI10.1007/s11128-020-02777-4
Indexed BySCI
Language英语
Funding ProjectNSFC[11671388] ; National Key Research Program[2018YFA0704705] ; National Natural Science Foundation of China[11471040] ; National Natural Science Foundation of China[11761131002]
WOS Research AreaPhysics
WOS SubjectQuantum Science & Technology ; Physics, Multidisciplinary ; Physics, Mathematical
WOS IDWOS:000557536200002
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/51944
Collection系统科学研究所
Corresponding AuthorZhao, Jiman
Affiliation1.Beijing Normal Univ, Key Lab Math & Complex Syst, Minist Educ, Sch Math Sci, Beijing 100875, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Ma, Guangsheng,Li, Hongbo,Zhao, Jiman. Quantum QR decomposition in the computational basis[J]. QUANTUM INFORMATION PROCESSING,2020,19(8):16.
APA Ma, Guangsheng,Li, Hongbo,&Zhao, Jiman.(2020).Quantum QR decomposition in the computational basis.QUANTUM INFORMATION PROCESSING,19(8),16.
MLA Ma, Guangsheng,et al."Quantum QR decomposition in the computational basis".QUANTUM INFORMATION PROCESSING 19.8(2020):16.
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