eigenvalue estimation
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2020 ◽  
Vol 20 (1&2) ◽  
pp. 14-36
Author(s):  
Souichi Takahira ◽  
Asuka Ohashi ◽  
Tomohiro Sogabe ◽  
Tsuyoshi S. Usuda

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 e^{\im A t}. However, the algorithm based on eigenvalue estimation needs \poly(1/\epsilon) runtime, where \epsilon is the desired accuracy of the output state. Moreover, if matrix A is not Hermitian, \e^{\im A t} 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/\epsilon)) and the algorithm outputs state |f> even if A is not Hermitian.


2019 ◽  
Vol 132 ◽  
pp. 172-180 ◽  
Author(s):  
N. Chentre ◽  
P. Saracco ◽  
S. Dulla ◽  
P. Ravetto

2016 ◽  
Vol 62 (7) ◽  
pp. 4300-4311 ◽  
Author(s):  
Ehsan Yazdian ◽  
Saeed Gazor ◽  
Mohammad Hasan Bastani ◽  
Mohsen Sharifitabar

Frequenz ◽  
2016 ◽  
Vol 70 (7-8) ◽  
Author(s):  
Jafar Mohammadi ◽  
Steffen Limmer ◽  
Sławomir Stańczak

AbstractThis paper considers eigenvalue estimation for the decentralized inference problem for spectrum sensing. We propose a decentralized eigenvalue computation algorithm based on the power method, which is referred to as


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