Fetching the paper…
Reading the bibliography…
We present a simplified exposition of some pieces of [Gily\'en, Su, Low, and Wiebe, STOC'19, arXiv:1806.01838], which introduced a quantum singular value transformation (QSVT) framework for applying polynomial functions to block-encoded matrices.
“Quantum algorithms for zero-sum games”
Joran van Apeldoorn and András Gilyén · 1904
Earlier work this paper cites.
“Sur l’ordre de la meilleure approximation des fonctions continues par les polynômes de degré donné”
S.. Bernstein · 1912
Earlier work this paper cites.
“Bessel functions and Kapteyn series”
G.. Watson · 1917
Earlier work this paper cites.
“Inequalities of A. Markoff and S. Bernstein for polynomials and related functions”
A.. Schaeffer · 1941
Earlier work this paper cites.
“Quantum algorithm for systems of linear equations with exponentially improved dependence on precision”
Andrew. Childs, Robin Kothari and Rolando. Somma · 1950
Earlier work this paper cites.
“Macroscopic approach to multichannel disordered conductors”
P.A Mello, P Pereyra and N Kumar · 1988
Earlier work this paper cites.
“Wave-packet approach to noise in multichannel mesoscopic systems”
Th. Martin and R. Landauer · 1992
Earlier work this paper cites.
“History and generality of the CS \mathrm{CS} decomposition”
C.. Paige and M. Wei · 1994
Earlier work this paper cites.
“A treatise on the theory of Bessel functions” Reprint of the second (1944) edition, Cambridge Mathematical Library
G.. Watson · 1995
Earlier work this paper cites.
“Random-matrix theory of quantum transport”
C… Beenakker · 1997
Cited alongside, same era.
“Chebyshev polynomials”
John Mason and David Handscomb · 2002
Cited alongside, same era.
“Quantum speed-up of markov chain based algorithms”
Mario Szegedy · 2004
Cited alongside, same era.
“Quantum computation lecture 2: Witness-preserving amplification of QMA” Accessed: 2022/12/20, 2006
Oded Regev · 2006
Cited alongside, same era.
“Quantum algorithm for linear systems of equations”
Aram. Harrow, Avinatan Hassidim and Seth Lloyd · 2009
Cited alongside, same era.
“Faster algorithms via approximation theory”
Sushant Sachdeva and Nisheeth. Vishnoi · 2014
Cited alongside, same era.
“Approximation theory and approximation practice, extended edition” Extended edition [of 3012510]
Lloyd. Trefethen · 2019
Later among the works it cites.
“Grand unification of quantum algorithms”
John. Martyn, Zane. Rossi, Andrew. Tan and Isaac. Chuang · 2021
Later among the works it cites.
“On solving classes of positive-definite quantum linear systems with quadratically improved runtime in the condition number”
Davide Orsucci and Vedran Dunjko · 2021
Later among the works it cites.
“Optimal-degree polynomial approximations for exponentials and gaussian kernel density estimation”
Amol Aggarwal and Josh Alman · 2022
Later among the works it cites.
“Lecture notes on quantum algorithms for scientific computation”, 2022
Lin Lin · 2022
Later among the works it cites.
URL: https://dlmf.nist.gov/
“ NIST Digital Library of Mathematical Functions · 2023
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Guang Low and Isaac. Chuang · 2017
Cited alongside, same era.
“Quantum singular value transformation and beyond: Exponential improvements for quantum matrix arithmetics”
András Gilyén, Yuan Su, Guang Low and Nathan Wiebe · 2019
Cited alongside, same era.
“Hamiltonian simulation by qubitization”
Guang Low and Isaac. Chuang · 2019
Cited alongside, same era.
“Essai sur la géométrie à n n dimensions”
Camille Jordan
Cited in the paper.
Closest in time.
“Quantum speedups for zero-sum games via improved dynamic gibbs sampling”
Adam Bouland et al · 2023
Closest in time.
“Fifty three matrix factorizations: a systematic approach”
Alan Edelman and Sungwoo Jeong · 2023
Closest in time.