Fetching the paper…
Reading the bibliography…
Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data.
Über das paulische äquivalenzverbot
P Jordan and E Wigner · 1928
Earlier work this paper cites.
Bounds for the quantity of information transmitted by a quantum communication channel
Alexander Semenovich Holevo · 1973
Earlier work this paper cites.
Simulating physics with computers
Richard P Feynman · 1982
Earlier work this paper cites.
Quantum theory, the Church–Turing principle and the universal quantum computer
David Deutsch · 1985
Earlier work this paper cites.
A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines
MF Hutchinson · 1990
Earlier work this paper cites.
Algorithms for quantum computation: discrete logarithms and factoring
Peter W Shor · 1994
Earlier work this paper cites.
A fast quantum mechanical algorithm for database search
Lov K Grover · 1996
Earlier work this paper cites.
Universal quantum simulators
Seth Lloyd · 1996
Earlier work this paper cites.
Fault-tolerant quantum computation
Peter W Shor · 1996
Earlier work this paper cites.
Tight bounds on quantum searching
Michel Boyer, Gilles Brassard, Peter Høyer, and Alain Tapp · 1998
Earlier work this paper cites.
Computing Betti numbers via combinatorial Laplacians
Joel Friedman · 1998
Earlier work this paper cites.
Power of one bit of quantum information
Emanuel Knill and Raymond Laflamme · 1998
Earlier work this paper cites.
The physical implementation of quantum computation
David P DiVincenzo · 2000
Earlier work this paper cites.
Combinatorial Laplacians of simplicial complexes
Timothy E Goldberg · 2002
Earlier work this paper cites.
Exact results for strongly correlated fermions in 2+ 1 dimensions
Paul Fendley and Kareljan Schoutens · 2005
Earlier work this paper cites.
Computing persistent homology
Afra Zomorodian and Gunnar Carlsson · 2005
Earlier work this paper cites.
Synthesis of quantum-logic circuits
Vivek V Shende, Stephen S Bullock, and Igor L Markov · 2006
Earlier work this paper cites.
Quantum t-designs: t-wise independence in the quantum world
Andris Ambainis and Joseph Emerson · 2007
Earlier work this paper cites.
Barcodes: the persistent topology of data
Robert Ghrist · 2008
Earlier work this paper cites.
Quantum algorithm for linear systems of equations
Aram W Harrow, Avinatan Hassidim, and Seth Lloyd · 2009
Earlier work this paper cites.
An introduction to quantum error correction and fault-tolerant quantum computation
Daniel Gottesman · 2010
Earlier work this paper cites.
Quantum Computation and Quantum Information
Michael A Nielsen and Isaac L Chuang · 2010
Earlier work this paper cites.
Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
Haim Avron and Sivan Toledo · 2011
Earlier work this paper cites.
Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
Frank Bauer, Jürgen Jost, and Shiping Liu · 2011
Earlier work this paper cites.
Quantum computational complexity
John Watrous · 2012
Earlier work this paper cites.
Efficient distributed quantum computing
Robert Beals, Stephen Brierley, Oliver Gray, Aram W Harrow, Samuel Kutin, Noah Linden, Dan Shepherd, and Mark Stather · 2013
Earlier work this paper cites.
Spectra of combinatorial Laplace operators on simplicial complexes
Danijela Horak and Jürgen Jost · 2013
Earlier work this paper cites.
Crackle: The homology of noise
Robert J Adler, Omer Bobrowski, and Shmuel Weinberger · 2014
Earlier work this paper cites.
The gudhi library: Simplicial complexes and persistent homology
Clément Maria, Jean-Daniel Boissonnat, Marc Glisse, and Mariette Yvinec · 2014
Earlier work this paper cites.
Hardness of classically simulating the one-clean-qubit model
Tomoyuki Morimae, Keisuke Fujii, and Joseph F Fitzsimons · 2014
Earlier work this paper cites.
A variational eigenvalue solver on a photonic quantum processor
Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien · 2014
Earlier work this paper cites.
Quantum support vector machine for big data classification
Patrick Rebentrost, Masoud Mohseni, and Seth Lloyd · 2014
Earlier work this paper cites.
Read the fine print
Scott Aaronson · 2015
Earlier work this paper cites.
Clique topology reveals intrinsic geometric structure in neural correlations
Chad Giusti, Eva Pastalkova, Carina Curto, and Vladimir Itskov · 2015
Cited alongside, same era.
Randomized block krylov methods for stronger and faster approximate singular value decomposition
Cameron Musco and Christopher Musco · 2015
Cited alongside, same era.
An introduction to quantum machine learning
Maria Schuld, Ilya Sinayskiy, and Francesco Petruccione · 2015
Cited alongside, same era.
On eigenvalues of random complexes
Anna Gundert and Uli Wagner · 2016
Cited alongside, same era.
Matthew Kahle · 2016
Cited alongside, same era.
Quantum algorithms for topological and geometric analysis of data
Seth Lloyd, Silvano Garnerone, and Paolo Zanardi · 2016
Approximation Theory and Approximation Practice, Extended Edition
Lloyd N Trefethen · 2019
Later among the works it cites.
Spectrum of the Laplacian on simplicial complexes by the Ricci curvature
Taiki Yamada · 2019
Later among the works it cites.
On the spectrum of dense random geometric graphs
Kartick Adhikari, Robert J Adler, Omer Bobrowski, and Ron Rosenthal · 2020
Later among the works it cites.
Spectral expansion of random sum complexes
Orr Beit-Aharon and Roy Meshulam · 2020
Later among the works it cites.
Quantum-inspired algorithms from randomized numerical linear algebra
Nadiia Chepurko, Kenneth L Clarkson, Lior Horesh, and David P Woodruff · 2020
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
The clique density theorem
Christian Reiher · 2016
Cited alongside, same era.
Fast methods for estimating the numerical rank of large matrices
Shashanka Ubaru and Yousef Saad · 2016
Cited alongside, same era.
Quantum machine learning
Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd · 2017
Cited alongside, same era.
Stochastic estimates for the trace of functions of matrices via Hadamard matrices
Paraskevi Fika and Christos Koukouvinos · 2017
Cited alongside, same era.
Eigenvalue confinement and spectral gap for random simplicial complexes
Antti Knowles and Ron Rosenthal · 2017
Cited alongside, same era.
Optimal Hamiltonian simulation by quantum signal processing
Guang Hao Low and Isaac L Chuang · 2017
Cited alongside, same era.
Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning
Nai-Hui Chia, András Gilyén, Tongyang Li, Han-Hsuan Lin, Ewin Tang, and Chunhao Wang · 2020
Later among the works it cites.
Towards quantum advantage for topological data analysis
Casper Gyurik, Chris Cade, and Vedran Dunjko · 2020
Later among the works it cites.
The spectral gaps of generalized flag complexes and a geometric Hall-type theorem
Alan Lew · 2020
Later among the works it cites.
A bayesian framework for persistent homology
Vasileios Maroulas, Farzana Nasrin, and Christopher Oballe · 2020
Later among the works it cites.
Topology of deep neural networks
Gregory Naitzat, Andrey Zhitnikov, and Lek-Heng Lim · 2020
Later among the works it cites.
Identification of relevant genetic alterations in cancer using topological data analysis
Raúl Rabadán, Yamina Mohamedi, Udi Rubin, Tim Chu, Adam N Alghalith, Oliver Elliott, Luis Arnés, Santiago Cal, Álvaro J Obaya, Arnold J Levine, et al · 2020
Later among the works it cites.
Measurement reduction in variational quantum algorithms
Andrew Zhao, Andrew Tranter, William M. Kirby, Shu Fay Ung, Akimasa Miyake, and Peter J. Love · 2020
Later among the works it cites.
Quantum computational advantage using photons
Han-Sen Zhong, Hui Wang, Yu-Hao Deng, Ming-Cheng Chen, Li-Chao Peng, Yi-Han Luo, Jian Qin, Dian Wu, Xing Ding, Yi Hu, et al · 2020
Later among the works it cites.
Quantum approximate optimization algorithm: Performance, mechanism, and implementation on near-term devices
Leo Zhou, Sheng-Tao Wang, Soonwon Choi, Hannes Pichler, and Mikhail D Lukin · 2020
Later among the works it cites.
Planck 2018 results. VI. Cosmological parameters
N. Aghanim et al · 2021
Later among the works it cites.
The Persistence of Large Scale Structures I: Primordial non-Gaussianity
Matteo Biagetti, Alex Cole, and Gary Shiu · 2021
Later among the works it cites.
Complexity of supersymmetric systems and the cohomology problem
Chris Cade and P Marcos Crichigno · 2021
Later among the works it cites.
Variational quantum algorithms
Marco Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, et al · 2021
Later among the works it cites.
A rigorous and robust quantum speed-up in supervised machine learning
Yunchao Liu, Srinivasan Arunachalam, and Kristan Temme · 2021
Later among the works it cites.
Quantum principal component analysis only achieves an exponential speedup because of its state preparation assumptions
Ewin Tang · 2021
Later among the works it cites.
Quantum topological data analysis with linear depth and exponential speedup
Shashanka Ubaru, Ismail Yunus Akhalwaya, Mark S Squillante, Kenneth L Clarkson, and Lior Horesh · 2021
Later among the works it cites.
Representation of the fermionic boundary operator
Ismail Yunus Akhalwaya, Yang-Hui He, Lior Horesh, Vishnu Jejjala, William Kirby, Kugendran Naidoo, and Shashanka Ubaru · 2022
Closest in time.
A (simple) classical algorithm for estimating betti numbers
Simon Apers, Sander Gribling, Sayantan Sen, and Dániel Szabó · 2022
Closest in time.
Clique homology is qma1-hard
Marcos Crichigno and Tamara Kohler · 2022
Closest in time.
Quantum computational advantage via high-dimensional gaussian boson sampling
Abhinav Deshpande, Arthur Mehta, Trevor Vincent, Nicolás Quesada, Marcel Hinsche, Marios Ioannou, Lars Madsen, Jonathan Lavoie, Haoyu Qi, Jens Eisert, et al · 2022
Closest in time.
Quantinuum H1 series trapped-ion quantum processor powered by honeywell
Honeywell · 2022
Closest in time.
Quantum advantage in learning from experiments
Hsin-Yuan Huang, Michael Broughton, Jordan Cotler, Sitan Chen, Jerry Li, Masoud Mohseni, Hartmut Neven, Ryan Babbush, Richard Kueng, John Preskill, et al · 2022
Closest in time.
Lecture notes on quantum algorithms for scientific computation
Lin Lin · 2022
Closest in time.
Quantum computational advantage with a programmable photonic processor
Lars S Madsen, Fabian Laudenbach, Mohsen Falamarzi Askarani, Fabien Rortais, Trevor Vincent, Jacob FF Bulmer, Filippo M Miatto, Leonhard Neuhaus, Lukas G Helt, Matthew J Collins, et al · 2022
Closest in time.
Statistical aspects of the quantum supremacy demonstration
Yosef Rinott, Tomer Shoham, and Gil Kalai · 2022
Closest in time.
Complexity-theoretic limitations on quantum algorithms for topological data analysis
Alexander Schmidhuber and Seth Lloyd · 2022
Closest in time.
Nature , 614(7949):676–681, 2023
Suppressing quantum errors by scaling a surface code logical qubit · 2023
Closest in time.
Promise clique homology on weighted graphs is QMA1-hard and contained in QMA
Robbie King and Tamara Kohler · 2023
Closest in time.