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Quantum kernel methods have been actively examined from both theoretical and practical perspectives due to the potential of quantum advantage in machine learning tasks.
No free lunch theorems for optimization
David H Wolpert and William G Macready · 1997
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A quantum adiabatic evolution algorithm applied to random instances of an np-complete problem
Edward Farhi, Jeffrey Goldstone, Sam Gutmann, Joshua Lapan, Andrew Lundgren, and Daniel Preda · 2001
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Quantum embeddings for machine learning
Seth Lloyd, Maria Schuld, Aroosa Ijaz, Josh Izaac, and Nathan Killoran · 2001
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The supervised learning no-free-lunch theorems
David H Wolpert · 2002
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Symmetric informationally complete quantum measurements
Joseph M Renes, Robin Blume-Kohout, Andrew J Scott, and Carlton M Caves · 2004
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Exact and approximate unitary 2-designs and their application to fidelity estimation
Christoph Dankert, Richard Cleve, Joseph Emerson, and Etera Livine · 2009
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Quantum support vector machine for big data classification
Patrick Rebentrost, Masoud Mohseni, and Seth Lloyd · 2014
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Average-case complexity versus approximate simulation of commuting quantum computations
Michael J Bremner, Ashley Montanaro, and Dan J Shepherd · 2016
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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 complexity of approximating complex-valued ising and tutte partition functions
Leslie Ann Goldberg and Heng Guo · 2017
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Barren plateaus in quantum neural network training landscapes
Jarrod R McClean, Sergio Boixo, Vadim N Smelyanskiy, Ryan Babbush, and Hartmut Neven · 2018
Earlier work this paper cites.
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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Quantum machine learning in feature hilbert spaces
Maria Schuld and Nathan Killoran · 2019
Earlier work this paper cites.
Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
Sukin Sim, Peter D Johnson, and Alán Aspuru-Guzik · 2019
Cited alongside, same era.
No free lunch theorem: A review
Stavros P Adam, Stamatios-Aggelos N Alexandropoulos, Panos M Pardalos, and Michael N Vrahatis · 2019
Cited alongside, same era.
Data re-uploading for a universal quantum classifier
Adrián Pérez-Salinas, Alba Cervera-Lierta, Elies Gil-Fuster, and José I Latorre · 2020
Cited alongside, same era.
Predicting many properties of a quantum system from very few measurements
Hsin-Yuan Huang, Richard Kueng, and John Preskill · 2020
Cited alongside, same era.
A rigorous and robust quantum speed-up in supervised machine learning
Yunchao Liu, Srinivasan Arunachalam, and Kristan Temme · 2021
Cited alongside, same era.
On the quantum versus classical learnability of discrete distributions
Exponential concentration and untrainability in quantum kernel methods
Supanut Thanasilp, Samson Wang, M Cerezo, and Zoë Holmes · 2022
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Bandwidth enables generalization in quantum kernel models
Abdulkadir Canatar, Evan Peters, Cengiz Pehlevan, Stefan M Wild, and Ruslan Shaydulin · 2022
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Connecting ansatz expressibility to gradient magnitudes and barren plateaus
Zoë Holmes, Kunal Sharma, Marco Cerezo, and Patrick J Coles · 2022
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On the practical usefulness of the hardware efficient ansatz
Lorenzo Leone, Salvatore FE Oliviero, Lukasz Cincio, and M Cerezo · 2022
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Diagnosing barren plateaus with tools from quantum optimal control
Martin Larocca, Piotr Czarnik, Kunal Sharma, Gopikrishnan Muraleedharan, Patrick J Coles, and Marco Cerezo · 2022
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Ryan Sweke, Jean-Pierre Seifert, Dominik Hangleiter, and Jens Eisert · 2021
Cited alongside, same era.
Supervised quantum machine learning models are kernel methods
Maria Schuld · 2021
Cited alongside, same era.
Noise-induced barren plateaus in variational quantum algorithms
Samson Wang, Enrico Fontana, Marco Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, and Patrick J Coles · 2021
Cited alongside, same era.
Effect of barren plateaus on gradient-free optimization
Andrew Arrasmith, Marco Cerezo, Piotr Czarnik, Lukasz Cincio, and Patrick J Coles · 2021
Cited alongside, same era.
Cost function dependent barren plateaus in shallow parametrized quantum circuits
Marco Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J Coles · 2021
Cited alongside, same era.
The inductive bias of quantum kernels
Jonas Kübler, Simon Buchholz, and Bernhard Schölkopf · 2021
Cited alongside, same era.
Barren plateaus preclude learning scramblers
Zoë Holmes, Andrew Arrasmith, Bin Yan, Patrick J Coles, Andreas Albrecht, and Andrew T Sornborger · 2021
Cited alongside, same era.
Later among the works it cites.
Representation theory for geometric quantum machine learning
Michael Ragone, Paolo Braccia, Quynh T Nguyen, Louis Schatzki, Patrick J Coles, Frederic Sauvage, Martin Larocca, and M Cerezo · 2022
Later among the works it cites.
Theoretical guarantees for permutation-equivariant quantum neural networks
Louis Schatzki, Martin Larocca, Frederic Sauvage, and Marco Cerezo · 2022
Later among the works it cites.
Theory for equivariant quantum neural networks
Quynh T Nguyen, Louis Schatzki, Paolo Braccia, Michael Ragone, Patrick J Coles, Frederic Sauvage, Martin Larocca, and M Cerezo · 2022
Later among the works it cites.
Approximate unitary t-designs by short random quantum circuits using nearest-neighbor and long-range gates
Aram W Harrow and Saeed Mehraban · 2023
Closest in time.
Qiskit: An open-source framework for quantum computing, 2023
Qiskit contributors · 2023
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Exploiting symmetry in variational quantum machine learning
Johannes Jakob Meyer, Marian Mularski, Elies Gil-Fuster, Antonio Anna Mele, Francesco Arzani, Alissa Wilms, and Jens Eisert · 2023
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Higher order derivatives of quantum neural networks with barren plateaus
Marco Cerezo and Patrick J Coles · 2058
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Equivalence of quantum barren plateaus to cost concentration and narrow gorges
Andrew Arrasmith, Zoë Holmes, Marco Cerezo, and Patrick J Coles · 2058
Closest in time.