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Dynamical Lie algebras (DLAs) have emerged as a valuable tool in the study of parameterized quantum circuits, helping to characterize both their expressiveness and trainability.
Algorithms for quantum computation: discrete logarithms and factoring
Peter W Shor · 1994
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Quantum cryptanalysis of hidden linear functions
Dan Boneh and Richard J Lipton · 1995
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Almost any quantum logic gate is universal
Seth Lloyd · 1995
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A fast quantum mechanical algorithm for database search
Lov K Grover · 1996
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Lie groups beyond an introduction
Anthony W Knapp and Anthony William Knapp · 1996
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Quantum computation of Fourier transforms over symmetric groups
Robert Beals · 1997
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Geometric control theory
Velimir Jurdjevic · 1997
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A quantum observable for the graph isomorphism problem
Mark Ettinger and Peter Hoyer · 1999
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A treatise on algebraic plane curves
Julian Lowell Coolidge · 2004
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Quantum computation and lattice problems
Oded Regev · 2004
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Introduction to Lie algebras
Karin Erdmann and Mark J Wildon · 2006
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Quantum algorithm for linear systems of equations
Aram W Harrow, Avinatan Hassidim, and Seth Lloyd · 2009
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An introduction to linear algebra
Leonid Mirsky · 2012
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Lie groups, Lie algebras, and representations
Brian C. Hall · 2013
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A quantum approximate optimization algorithm
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann · 2014
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Real forms of simple lie algebras
Kaushalya Rani Hota · 2014
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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
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Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M Chow, and Jay M Gambetta · 2017
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Controllability of symmetric spin networks
Francesca Albertini and Domenico D’Alessandro · 2018
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Quantum approximate optimization is computationally universal
Seth Lloyd · 2018
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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
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Quantum-assisted quantum compiling
Sumeet Khatri, Ryan LaRose, Alexander Poremba, Lukasz Cincio, Andrew T Sornborger, and Patrick J Coles · 2019
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A simple method for finding the inverse matrix of Vandermonde matrix
Edris Ahmad Rawashdeh · 2019
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Learning unitaries by gradient descent
Bobak Toussi Kiani, Seth Lloyd, and Reevu Maity · 2020
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On the universality of the quantum approximate optimization algorithm
Mauro ES Morales, Jacob D Biamonte, and Zoltán Zimborás · 2020
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Exploring entanglement and optimization within the Hamiltonian variational ansatz
Roeland Wiersema, Cunlu Zhou, Yvette de Sereville, Juan Felipe Carrasquilla, Yong Baek Kim, and Henry Yuen · 2020
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Trainability of dissipative perceptron-based quantum neural networks
Kunal Sharma, Marco Cerezo, Lukasz Cincio, and Patrick J Coles · 2022
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Importance of kernel bandwidth in quantum machine learning
Ruslan Shaydulin and Stefan M Wild · 2022
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Efficient classical algorithms for simulating symmetric quantum systems
Eric R Anschuetz, Andreas Bauer, Bobak T Kiani, and Seth Lloyd · 2023
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Showcasing a barren plateau theory beyond the dynamical Lie algebra
NL Diaz, Diego García-Martín, Sujay Kazi, Martin Larocca, and M Cerezo · 2023
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The adjoint is all you need: Characterizing barren plateaus in quantum ansatze
Enrico Fontana, Dylan Herman, Shouvanik Chakrabarti, Niraj Kumar, Romina Yalovetzky, Jamie Heredge, Shree Hari Sureshbabu, and Marco Pistoia · 2023
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The power of quantum neural networks
Amira Abbas, David Sutter, Christa Zoufal, Aurélien Lucchi, Alessio Figalli, and Stefan Woerner · 2021
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Focus beyond quadratic speedups for error-corrected quantum advantage
Ryan Babbush, Jarrod R McClean, Michael Newman, Craig Gidney, Sergio Boixo, and Hartmut Neven · 2021
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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
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Quantum-optimal-control-inspired ansatz for variational quantum algorithms
Alexandre Choquette, Agustin Di Paolo, Panagiotis Kl Barkoutsos, David Sénéchal, Ivano Tavernelli, and Alexandre Blais · 2021
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Cost function dependent barren plateaus in shallow parametrized quantum circuits
Marco Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J Coles · 2021
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Barren plateaus preclude learning scramblers
Zoë Holmes, Andrew Arrasmith, Bin Yan, Patrick J Coles, Andreas Albrecht, and Andrew T Sornborger · 2021
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Quantum algorithm zoo
Stephen Jordan · 2021
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Quantum neural network cost function concentration dependency on the parametrization expressivity
Lucas Friedrich and Jonas Maziero · 2023
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Disentangling hype from practicality: On realistically achieving quantum advantage
Torsten Hoefler, Thomas Häner, and Matthias Troyer · 2023
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The impact of cost function globality and locality in hybrid quantum neural networks on NISQ devices
Muhammad Kashif and Saif Al-Kuwari · 2023
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Theory of overparametrization in quantum neural networks
Martin Larocca, Nathan Ju, Diego García-Martín, Patrick J Coles, and Marco Cerezo · 2023
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Trainability and expressivity of Hamming-weight preserving quantum circuits for machine learning
Léo Monbroussou, Jonas Landman, Alex B Grilo, Romain Kukla, and Elham Kashefi · 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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Barren plateaus in quantum tensor network optimization
Enrique Cervero Martín, Kirill Plekhanov, and Michael Lubasch · 2023
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A unified theory of barren plateaus for deep parametrized quantum circuits
Michael Ragone, Bojko N Bakalov, Frédéric Sauvage, Alexander F Kemper, Carlos Ortiz Marrero, Martin Larocca, and M Cerezo · 2023
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Subtleties in the trainability of quantum machine learning models
Supanut Thanasilp, Samson Wang, Nhat Anh Nghiem, Patrick Coles, and Marco Cerezo · 2023
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Roeland Wiersema, Efekan Kökcü, Alexander F Kemper, and Bojko N Bakalov · 2023
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A review on quantum approximate optimization algorithm and its variants
Kostas Blekos, Dean Brand, Andrea Ceschini, Chiao-Hui Chou, Rui-Hao Li, Komal Pandya, and Alessandro Summer · 2024
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Effects of noise on the overparametrization of quantum neural networks
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On the universality of Sn-equivariant k-body gates
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Theory for equivariant quantum neural networks
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Theoretical guarantees for permutation-equivariant quantum neural networks
Louis Schatzki, Martin Larocca, Quynh T Nguyen, Frederic Sauvage, and Marco Cerezo · 2024
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