論文

査読有り
2020年

Quantum algorithm for matrix functions by Cauchy's integral formula.

Quantum Information & Computation
  • Souichi Takahira
  • ,
  • Asuka Ohashi
  • ,
  • Tomohiro Sogabe
  • ,
  • Tsuyoshi Sasaki Usuda

20
1&2
開始ページ
14
終了ページ
36
記述言語
英語
掲載種別
研究論文(学術雑誌)
出版者・発行元
RINTON PRESS, INC

© Rinton Press. For matrix A, vector b and function f, the computation of vector f(A)b arises in many scientific computing applications. We consider the problem of obtaining quantum state |f〉corresponding to vector f(A)b. There is a quantum algorithm to compute state |f〉 using eigenvalue estimation that uses phase estimation and Hamiltonian simulation eiAt. However, the algorithm based on eigenvalue estimation needs poly(1/ɛ) runtime, where ɛ is the desired accuracy of the output state. Moreover, if matrix A is not Hermitian, eiAt is not unitary and we cannot run eigenvalue estimation. In this paper, we propose a quantum algorithm that uses Cauchy’s integral formula and the trapezoidal rule as an approach that avoids eigenvalue estimation. We show that the runtime of the algorithm is poly(log(1/ɛ)) and the algorithm outputs state |f〉 even if A is not Hermitian.


リンク情報
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000510617200002&DestApp=WOS_CPL
URL
http://www.rintonpress.com/xxqic20/qic-20-12/0014-0036.pdf
Dblp Url
https://dblp.uni-trier.de/db/journals/qic/qic20.html#TakahiraOSU20
Scopus
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85079121558&origin=inward
Scopus Citedby
https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85079121558&origin=inward
ID情報
  • ISSN : 1533-7146
  • DBLP ID : journals/qic/TakahiraOSU20
  • SCOPUS ID : 85079121558
  • Web of Science ID : WOS:000510617200002

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