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

14

36

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
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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