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Quantum computing offers the potential of exponential speedups for certain classical computations.
Über das paulische äquivalenzverbot
P Jordan and E Wigner · 1928
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A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines
MF Hutchinson · 1990
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Calculating the density of states and optical-absorption spectra of large quantum systems by the plane-wave moments method
Lin-Wang Wang · 1994
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Universal quantum simulators
Seth Lloyd · 1996
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Computing Betti numbers via combinatorial Laplacians
Joel Friedman · 1998
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Tight bounds on quantum searching
Michel Boyer, Gilles Brassard, Peter Høyer, and Alain Tapp · 1998
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Fermionic quantum computation
Sergey B Bravyi and Alexei Yu Kitaev · 2002
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Combinatorial Laplacians of simplicial complexes
Timothy E Goldberg · 2002
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Computing persistent homology
Afra Zomorodian and Gunnar Carlsson · 2005
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Quantum t-designs: t-wise independence in the quantum world
Andris Ambainis and Joseph Emerson · 2007
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Barcodes: the persistent topology of data
Robert Ghrist · 2008
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Quantum Computation and Quantum Information
Michael A Nielsen and Isaac L Chuang · 2010
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Simulation of electronic structure hamiltonians using quantum computers
James D Whitfield, Jacob Biamonte, and Alán Aspuru-Guzik · 2011
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Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
Haim Avron and Sivan Toledo · 2011
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Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
Frank Bauer, Jürgen Jost, and Shiping Liu · 2011
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Spectra of combinatorial Laplace operators on simplicial complexes
Danijela Horak and Jürgen Jost · 2013
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An introduction to quantum machine learning
Maria Schuld, Ilya Sinayskiy, and Francesco Petruccione · 2015
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Read the fine print
Scott Aaronson · 2015
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Statistical topological data analysis using persistence landscapes
Peter Bubenik · 2015
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Quantum algorithms for topological and geometric analysis of data
Seth Lloyd, Silvano Garnerone, and Paolo Zanardi · 2016
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Fast methods for estimating the numerical rank of large matrices
Shashanka Ubaru and Yousef Saad · 2016
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The clique density theorem
Christian Reiher · 2016
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On eigenvalues of random complexes
Anna Gundert and Uli Wagner · 2016
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Matthew Kahle · 2016
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Efficient estimation of eigenvalue counts in an interval
Edoardo Di Napoli, Eric Polizzi, and Yousef Saad · 2016
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Approximating spectral densities of large matrices
Lin Lin, Yousef Saad, and Chao Yang · 2016
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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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Parameterized quantum circuits as machine learning models
Marcello Benedetti, Erika Lloyd, Stefan Sack, and Mattia Fiorentini · 2019
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A quantum-inspired classical algorithm for recommendation systems
Ewin Tang · 2019
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Review of a quantum algorithm for Betti numbers
Sam Gunn and Niels Kornerup · 2019
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Lek-Heng Lim · 2019
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Quantum machine learning
Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd · 2017
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The quantum complexity of computing Schatten p p -norms
Chris Cade and Ashley Montanaro · 2017
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Optimal Hamiltonian simulation by quantum signal processing
Guang Hao Low and Isaac L Chuang · 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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Stochastic estimates for the trace of functions of matrices via Hadamard matrices
Paraskevi Fika and Christos Koukouvinos · 2017
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Eigenvalue confinement and spectral gap for random simplicial complexes
Antti Knowles and Ron Rosenthal · 2017
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Zvika Brakerski and Omri Shmueli · 2019
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Approximation Theory and Approximation Practice, Extended Edition
Lloyd N Trefethen · 2019
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Spectrum of the Laplacian on simplicial complexes by the Ricci curvature
Taiki Yamada · 2019
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Training deep quantum neural networks
Kerstin Beer, Dmytro Bondarenko, Terry Farrelly, Tobias J Osborne, Robert Salzmann, Daniel Scheiermann, and Ramona Wolf · 2020
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A rigorous and robust quantum speed-up in supervised machine learning
Yunchao Liu, Srinivasan Arunachalam, and Kristan Temme · 2020
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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
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Quantum-inspired algorithms from randomized numerical linear algebra
Nadiia Chepurko, Kenneth L Clarkson, Lior Horesh, and David P Woodruff · 2020
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Towards quantum advantage for topological data analysis
Casper Gyurik, Chris Cade, and Vedran Dunjko · 2020
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Circuit optimization of hamiltonian simulation by simultaneous diagonalization of Pauli clusters
Ewout van den Berg and Kristan Temme · 2020
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Spectral gaps, missing faces and minimal degrees
Alan Lew · 2020
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The spectral gaps of generalized flag complexes and a geometric Hall-type theorem
Alan Lew · 2020
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On the spectrum of dense random geometric graphs
Kartick Adhikari, Robert J Adler, Omer Bobrowski, and Ron Rosenthal · 2020
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Spectral expansion of random sum complexes
Orr Beit-Aharon and Roy Meshulam · 2020
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Term grouping and travelling salesperson for digital quantum simulation
Kaiwen Gui, Teague Tomesh, Pranav Gokhale, Yunong Shi, Frederic T Chong, Margaret Martonosi, and Martin Suchara · 2021
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