Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Elsevier eBooks

Standard r-Transformation Matrices and Their Applications

U. Fano, A. R. P. Rau

Published Jan 1, 1996• 0 citations
Publisher
DOI
10.1016/b978-012248455-1/50005-1

Related papers

Machine Learning the period finding algorithm

John George Francis, Anil Shaji

We use differentiable programming and gradient descent to find unitary matrices that can be used in the period finding algorithm to extract period information from the state of a quantum computer post application of the oracle. The standard procedure is to use the inverse quantum Fourier transform. Our findings suggest that that this is not the only unitary matrix appropriate for the period finding algorithm, There exist several unitary matrices that can affect out the same transformation and they are significantly different from each other as well. These unitary matrices can be learned by an algorithm. Neural networks can be applied to differentiate such unitary matrices from randomly generated ones indicating that these unitaries do have characteristic features that cannot otherwise be discerned easily.

arXiv:2103.05708•Mar 9, 2021•0 citations

THE CONNECTION BETWEEN THE R-MATRIX AND THE S-MATRIX

N. G. van Kampen

Revista Mexicana de Física•Oct 1, 1953•5 citations

The t-Matrix and the Canonical Transformation

Roger Balian

•Jan 1, 1962•0 citations

A standard form for generalised CP transformations

Gerhard Franz Ecker, Walter Grimus, Helmut Neufeld

The investigation of general CP transformations leads to transformations of the form U to WTUW with unitary matrices U, W. It is shown that a basis of weak eigenstates can always be chosen such that WTUW has a certain real standard form.

Journal of Physics A Mathematical and General•Aug 21, 1987•114 citations

Generalized quantum singular value transformation with application in quantum conjugate gradient least squares algorithm

Yu-Qiu Liu, Hefeng Wang, Xiang, Hua

Quantum signal processing (QSP) and generalized quantum signal processing (GQSP) are essential tools for implementing the block encoding of matrix functions. The achievable polynomials of QSP have restrictions on parity, while GQSP eliminates these restrictions. But GQSP only constructs functions of unitary matrices. In this paper, we further investigate GQSP and extend it to general matrices. Compared with the quantum singular value transformation (QSVT), our proposed method relaxes the requirements on the parity of polynomials. We refer to this extension as generalized quantum singular value transformation (GQSVT). Subsequently, by utilizing the relationship between generalized matrix functions and standard matrix functions, we propose a classical-quantum hybrid quantum conjugate gradient least squares (CGLS) algorithm using GQSVT.

arXiv:2508.21390•Aug 29, 2025•0 citations

Application of the Infinite Product Representation of the R-Matrix

Jinchu Huang

•Jan 1, 1989•0 citations
We use differentiable programming and gradient descent to find unitary matrices that can be used in the period finding algorithm to extract period information from the state of a quantum computer post application of the oracle. The standard procedure is to use the inverse quantum Fourier transform. Our findings suggest that that this is not the only unitary matrix appropriate for the period finding algorithm, There exist several unitary matrices that can affect out the same transformation and they are significantly different from each other as well. These unitary matrices can be learned by an algorithm. Neural networks can be applied to differentiate such unitary matrices from randomly generated ones indicating that these unitaries do have characteristic features that cannot otherwise be discerned easily.
Quantum signal processing (QSP) and generalized quantum signal processing (GQSP) are essential tools for implementing the block encoding of matrix functions. The achievable polynomials of QSP have restrictions on parity, while GQSP eliminates these restrictions. But GQSP only constructs functions of unitary matrices. In this paper, we further investigate GQSP and extend it to general matrices. Compared with the quantum singular value transformation (QSVT), our proposed method relaxes the requirements on the parity of polynomials. We refer to this extension as generalized quantum singular value transformation (GQSVT). Subsequently, by utilizing the relationship between generalized matrix functions and standard matrix functions, we propose a classical-quantum hybrid quantum conjugate gradient least squares (CGLS) algorithm using GQSVT.