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Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce.
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Sam Gunn and Niels Kornerup · 1906
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Rolando D Somma · 1907
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Seth Lloyd · 1996
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Joel Friedman · 1998
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Emanuel Knill and Raymond Laflamme · 1998
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“Quantum algorithms for quantum chemistry and quantum materials science”
Bela Bauer, Sergey Bravyi, Mario Motta, and Garnet Kin Chan · 2001
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Timothy E Goldberg · 2002
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“Classical and quantum computation”
Alexei Yu Kitaev, Alexander Shen, Mikhail N Vyalyi, and Mikhail N Vyalyi · 2002
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Jianer Chen, Xiuzhen Huang, Iyad A Kanj, and Ge Xia · 2006
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“Several natural BQP-complete problems” (2006)
Pawel Wocjan and Shengyu Zhang · 2006
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“Hybrid divide-and-conquer approach for tree search algorithms” (2020)
Mathys Rennela, Alfons Laarman, and Vedran Dunjko · 2007
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“The rank of a random matrix”
Xinlong Feng and Zhinan Zhang · 2007
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“Barcodes: the persistent topology of data”
Robert Ghrist · 2008
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“Entanglement theory and the quantum simulation of many-body physics”
Fernando GSL Brandão · 2008
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“Estimating Jones polynomials is a complete problem for one clean qubit”
Peter W Shor and Stephen P Jordan · 2008
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“Quantum algorithm for linear systems of equations”
Aram W Harrow, Avinatan Hassidim, and Seth Lloyd · 2009
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László Lovász et al · 2009
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“Simplicial matrix-tree theorems”
Art Duval, Caroline Klivans, and Jeremy Martin · 2009
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“Quantifying complexity in networks: the von Neumann entropy”
Filippo Passerini and Simone Severini · 2009
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“On the quantum complexity of evaluating the Tutte polynomial”
Hamed Ahmadi and Pawel Wocjan · 2010
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“Error mitigation via verified phase estimation”
Thomas E O’Brien, Stefano Polla, Nicholas C Rubin, William J Huggins, Sam McArdle, Sergio Boixo, Jarrod R McClean, and Ryan Babbush · 2010
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“Focus beyond quadratic speedups for error-corrected quantum advantage”
Ryan Babbush, Jarrod McClean, Craig Gidney, Sergio Boixo, and Hartmut Neven · 2011
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“Quantum computation and quantum information”
Michael A. Nielsen and Isaac L. Chuang · 2011
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“Computational difficulty of computing the density of states”
Brielin Brown, Steven T Flammia, and Norbert Schuch · 2011
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Nathan Halko, Per-Gunnar Martinsson, and Joel A Tropp · 2011
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“Estimating the unseen: an n/log(n)-sample estimator for entropy and support size, shown optimal via new clts”
Gregory Valiant and Paul Valiant · 2011
Tomoyuki Morimae · 2017
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“Fast estimation of approximate matrix ranks using spectral densities”
Shashanka Ubaru, Yousef Saad, and Abd-Krim Seghouane · 2017
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“Simplicial complexes: spectrum, homology and random walks”
Ori Parzanchevski and Ron Rosenthal · 2017
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“Spectral sparsification of simplicial complexes for clustering and label propagation”
Braxton Osting, Sourabh Palande, and Bei Wang · 2017
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“Almost Optimal Bounds for Sublinear-Time Sampling of k-Cliques in Bounded Arboricity Graphs”
Talya Eden, Dana Ron, and Will Rosenbaum · 2012
Cited alongside, same era.
“Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks”
Slobodan Maletić and Milan Rajković · 2012
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“Spectra of combinatorial Laplace operators on simplicial complexes”
Danijela Horak and Jürgen Jost · 2013
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“Fast matrix rank algorithms and applications”
Ho Yee Cheung, Tsz Chiu Kwok, and Lap Chi Lau · 2013
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“Subgraph frequencies: Mapping the empirical and extremal geography of large graph collections”
Johan Ugander, Lars Backstrom, and Jon Kleinberg · 2013
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“Perturbation theory for linear operators”
Tosio Kato · 2013
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“Quantum principal component analysis”
Seth Lloyd, Masoud Mohseni, and Patrick Rebentrost · 2014
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Kristan Temme, Sergey Bravyi, and Jay M Gambetta · 2017
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“Quantum computing in the NISQ era and beyond”
John Preskill · 2018
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“The quantum complexity of computing Schatten p p -norms”
Chris Cade and Ashley Montanaro · 2018
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“Approximating the spectrum of a graph”
David Cohen-Steiner, Weihao Kong, Christian Sohler, and Gregory Valiant · 2018
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“The quantum Theil index: characterizing graph centralization using von Neumann entropy”
David Simmons, Justin Coon, and Animesh Datta · 2018
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“Low-cost error mitigation by symmetry verification”
Xavi Bonet-Monroig, Ramiro Sagastizabal, M Singh, and TE O’Brien · 2018
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“Practical quantum error mitigation for near-future applications”
Suguru Endo, Simon C Benjamin, and Ying Li · 2018
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“Demonstration of topological data analysis on a quantum processor”
He-Liang Huang, Xi-Lin Wang, Peter P Rohde, Yi-Han Luo, You-Wei Zhao, Chang Liu, Li Li, Nai-Le Liu, Chao-Yang Lu, and Jian-Wei Pan · 2018
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“Supervised learning with quantum-enhanced feature spaces”
Vojtěch Havlíček, Antonio D Córcoles, Kristan Temme, Aram W Harrow, Abhinav Kandala, Jerry M Chow, and Jay M Gambetta · 2019
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“A quantum-inspired classical algorithm for recommendation systems”
Ewin Tang · 2019
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“Clustering-independent analysis of genomic data using spectral simplicial theory”
Kiya W Govek, Venkata S Yamajala, and Pablo G Camara · 2019
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András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe · 2019
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Shantanav Chakraborty, András Gilyén, and Stacey Jeffery · 2019
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“Complex networks from classical to quantum”
Jacob Biamonte, Mauro Faccin, and Manlio De Domenico · 2019
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Jayadev Acharya, Ibrahim Issa, Nirmal V Shende, and Aaron B Wagner · 2019
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“Error-mitigated digital quantum simulation”
Sam McArdle, Xiao Yuan, and Simon Benjamin · 2019
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“Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments”
Thomas E. O’Brien, Brian Tarasinski, and Barbara Terhal · 2019
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“A non-review of quantum machine learning: trends and explorations”
Vedran Dunjko and Peter Wittek · 2020
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“Circuit-centric quantum classifiers”
Maria Schuld, Alex Bocharov, Krysta M Svore, and Nathan Wiebe · 2020
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“Quantum gradient descent for linear systems and least squares”
Iordanis Kerenidis and Anupam Prakash · 2020
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“Complexity of supersymmetric systems and the cohomology problem” (2021)
Chris Cade and P Marcos Crichigno · 2021
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“Electronic structure in a fixed basis is qma-complete”
Bryan O’Gorman, Sandy Irani, James Whitfield, and Bill Fefferman · 2021
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“Quantum topological data analysis with linear depth and exponential speedup” (2021)
Shashanka Ubaru, Ismail Yunus Akhalwaya, Mark S Squillante, Kenneth L Clarkson, and Lior Horesh · 2021
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Alicja Dutkiewicz, Barbara M Terhal, and Thomas E O’Brien · 2021
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