Quantum machine learning with subspace states

I Kerenidis, A Prakash - arXiv preprint arXiv:2202.00054, 2022 - arxiv.org
We introduce a new approach for quantum linear algebra based on quantum subspace
states and present three new quantum machine learning algorithms. The first is a quantum …

[图书][B] A Journey through the History of Numerical Linear Algebra

C Brezinski, G Meurant, M Redivo-Zaglia - 2022 - SIAM
A Journey through the History of Numerical Linear Algebra: Back Matter Page 1 Bibliography
[1] A. Abdelfattah, H. Anzt, A. Bouteiller, A. Danalis, JJ Dongarra, M. Gates, A. Haidar, J. Kurzak …

Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer

CH Chee, D Leykam, AM Mak, DG Angelakis - Physical Review A, 2023 - APS
Fermionic Ansatz state preparation is a critical subroutine in many quantum algorithms such
as the variational quantum eigensolver for quantum chemistry and condensed-matter …

Zolotarev iterations for the matrix square root

ES Gawlik - SIAM journal on matrix analysis and applications, 2019 - SIAM
We construct a family of iterations for computing the principal square root of a square matrix
A using Zolotarev's rational minimax approximants of the square root function. We show that …

Simpler Grassmannian optimization

Z Lai, LH Lim, K Ye - arXiv preprint arXiv:2009.13502, 2020 - arxiv.org
There are two widely used models for the Grassmannian $\operatorname {Gr}(k, n) $, as the
set of equivalence classes of orthogonal matrices $\operatorname {O}(n)/(\operatorname …

Rational Minimax Iterations for Computing the Matrix pth Root

ES Gawlik - Constructive Approximation, 2021 - Springer
In a previous paper by the author, a family of iterations for computing the matrix square root
was constructed by exploiting a recursion obeyed by Zolotarev's rational minimax …

Time-varying polar decomposition by continuous-time model and discrete-time algorithm of zeroing neural network using Zhang time discretization (ZTD)

Z Tang, L Ming, Y Zhang, R Shi - 2021 11th International …, 2021 - ieeexplore.ieee.org
Time-varying polar decomposition becomes important and has many applications in
potential fields. This paper first proposes a continuous-time model and a discrete-time …

Algebraic and Differential Geometry in Modern Optimization

Z Lai - 2023 - search.proquest.com
Stochastic optimization algorithms have become indispensable in modern machine
learning. The developments of theories and algorithms of modern optimization also requires …

[PDF][PDF] RESOURCE-EFFICIENT QUANTUM ALGORITHMS FOR QUANTUM CHEMISTRY

CC Hian - 2024 - dimitrisangelakis.org
Quantum mechanics lies at the foundation of all modern chemistry, but we have yet to
efficiently use it to accurately predict chemical properties of compounds. As Dirac noted …

Iterations for the Unitary Sign Decomposition and the Unitary Eigendecomposition

ES Gawlik - arXiv preprint arXiv:2011.12449, 2020 - arxiv.org
We construct fast, structure-preserving iterations for computing the sign decomposition of a
unitary matrix $ A $ with no eigenvalues equal to $\pm i $. This decomposition factorizes $ A …