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Quantum signal processing (QSP) is a framework which was proven to unify and simplify a large number of known quantum algorithms, as well as discovering new ones.
“A Fast Quantum Mechanical Algorithm for Database Search”
Lov K. Grover · 1996
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“Quantum Amplitude Amplification and Estimation”
Gilles Brassard, Peter Hoyer, Michele Mosca, and Alain Tapp · 2002
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“Finding Angles for Quantum Signal Processing with Machine Precision” (2020)
Rui Chao, Dawei Ding, Andras Gilyen, Cupjin Huang, and Mario Szegedy · 2003
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“Quantum speed-up of Markov chain based algorithms”
Mario Szegedy · 2004
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“Quantum walk algorithm for element distinctness”
A Ambainis · 2004
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“Positive extensions, Fejér-Riesz factorization and autoregressive filters in two variables”
Jeffrey S. Geronimo and Hugo J. Woerdeman · 2004
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“Quantum Algorithm for Linear Systems of Equations”
Aram W. Harrow, Avinatan Hassidim, and Seth Lloyd · 2009
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“Fourier Analysis: An Introduction”
Elias M. Stein and Rami Shakarchi · 2011
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“Hamiltonian simulation using linear combinations of unitary operations”
Andrew M Childs and Nathan Wiebe · 2012
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“Sinkhorn normal form for unitary matrices”
Martin Idel and Michael M. Wolf · 2015
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“Methodology of Resonant Equiangular Composite Quantum Gates”
Guang Hao Low, Theodore J. Yoder, and Isaac L. Chuang · 2016
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“Quantum signal processing by single-qubit dynamics”
Guang Hao Low · 2017
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“Optimal Hamiltonian Simulation by Quantum Signal Processing”
Guang Hao Low and Isaac L. Chuang · 2017
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“Hamiltonian Simulation by Uniform Spectral Amplification” (2017)
Guang Hao Low and Isaac L Chuang · 2017
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“Quantum singular value transformation and beyond: Exponential improvements for quantum matrix arithmetics”
András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe · 2019
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“Hamiltonian Simulation by Qubitization”
Guang Hao Low and Isaac L Chuang · 2019
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“Product Decomposition of Periodic Functions in Quantum Signal Processing”
Jeongwan Haah · 2019
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“Span programs and quantum time complexity”
Arjan Cornelissen, Stacey Jeffery, Maris Ozols, and Alvaro Piedrafita · 2020
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“A Unified Framework of Quantum Walk Search”
Simon Apers, András Gilyén, and Stacey Jeffery · 2021
Cited alongside, same era.
“A Grand Unification of Quantum Algorithms”
John M. Martyn, Zane M. Rossi, Andrew K. Tan, and Isaac L. Chuang · 2021
Cited alongside, same era.
“Hamiltonian singular value transformation and inverse block encoding” (2021)
Seth Lloyd, Bobak T. Kiani, David R. M. Arvidsson-Shukur, Samuel Bosch, Giacomo De Palma, William M. Kaminsky, Zi-Wen Liu, and Milad Marvian · 2021
“Semantic embedding for quantum algorithms”
Zane M. Rossi and Isaac L. Chuang · 2023
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“Modular quantum signal processing in many variables” (2023)
Zane M. Rossi, Jack L. Ceroni, and Isaac L. Chuang · 2023
Later among the works it cites.
“Quantum signal processing with continuous variables” (2023)
Zane M Rossi, Victor M Bastidas, William J Munro, and Isaac L Chuang · 2023
Later among the works it cites.
“On variants of multivariate quantum signal processing and their characterizations” (2023)
Balázs Németh, Blanka Kövér, Boglárka Kulcsár, Roland Botond Miklósi, and András Gilyén · 2023
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“A Quantum Algorithm for Functions of Multiple Commuting Hermitian Matrices” (2023)
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“Efficient phase-factor evaluation in quantum signal processing”
Yulong Dong, Xiang Meng, K Birgitta Whaley, and Lin Lin · 2021
Cited alongside, same era.
“Fejer-Riesz Theorem and Its Generalization”
Abdulmtalb Hussen and Abdelbaset Zeyani · 2021
Cited alongside, same era.
“Quantum divide and conquer” (2022)
Andrew M Childs, Robin Kothari, Matt Kovacs-Deak, Aarthi Sundaram, and Daochen Wang · 2022
Cited alongside, same era.
“Quantum state preparation without coherent arithmetic” (2022)
Sam McArdle, András Gilyén, and Mario Berta · 2022
Cited alongside, same era.
“On the energy landscape of symmetric quantum signal processing”
Jiasu Wang, Yulong Dong, and Lin Lin · 2022
Cited alongside, same era.
“Multivariable quantum signal processing (M-QSP): Prophecies of the two-headed oracle”
Zane M. Rossi and Isaac L. Chuang · 2022
Cited alongside, same era.
Yonah Borns-Weil, Tahsin Saffat, and Zachary Stier · 2023
Later among the works it cites.
“A CS guide to the quantum singular value transformation” (2023)
Ewin Tang and Kevin Tian · 2023
Later among the works it cites.
“Taming Quantum Time Complexity”
Aleksandrs Belovs, Stacey Jeffery, and Duyal Yolcu · 2024
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“Infinite quantum signal processing”
Yulong Dong, Lin Lin, Hongkang Ni, and Jiasu Wang · 2024
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“Recursive quantum eigenvalue and singular-value transformation: Analytic construction of matrix sign function by Newton iteration”
Kaoru Mizuta and Keisuke Fujii · 2024
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“Generalized Quantum Signal Processing”
Danial Motlagh and Nathan Wiebe · 2024
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“Quantum signal processing over SU(N)” (2024)
Lorenzo Laneve · 2024
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“Complexification of Quantum Signal Processing and its Ramifications” (2024)
V. M. Bastidas and K. J. Joven · 2024
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“Comment on "Multivariable quantum signal processing (M-QSP): Prophecies of the two-headed oracle"”
Hitomi Mori, Kaoru Mizuta, and Keisuke Fujii · 2024
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“Doubling the efficiency of Hamiltonian simulation via generalized quantum signal processing”
Dominic W. Berry, Danial Motlagh, Giacomo Pantaleoni, and Nathan Wiebe · 2024
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