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The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography.
Bounds for the quantity of information transmitted by a quantum communication channel
Alexander Semenovich Holevo · 1973
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Quantum-state tomography and discrete wigner function
Ulf Leonhardt · 1995
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Quantum error correction and orthogonal geometry
A Robert Calderbank, Eric M Rains, Peter W Shor, and Neil JA Sloane · 1997
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Elements of information theory
Thomas M Cover · 1999
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The nature of statistical learning theory
Vladimir Vapnik · 1999
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Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps
Michał Horodecki, Paweł Horodecki, and Ryszard Horodecki · 2001
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Ancilla-assisted quantum process tomography
Joseph B Altepeter, David Branning, Evan Jeffrey, TC Wei, Paul G Kwiat, Robert T Thew, Jeremy L O’Brien, Michael A Nielsen, and Andrew G White · 2003
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Improved simulation of stabilizer circuits
Scott Aaronson and Daniel Gottesman · 2004
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Universal quantum circuit for two-qubit transformations with three controlled-not gates
G. Vidal and C. M. Dawson · 2004
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Pattern recognition and machine learning
Christopher M Bishop and Nasser M Nasrabadi · 2006
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The learnability of quantum states
Scott Aaronson · 2007
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Random features for large-scale kernel machines
Ali Rahimi and Benjamin Recht · 2007
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Quantum-process tomography: Resource analysis of different strategies
Masoud Mohseni, Ali T Rezakhani, and Daniel A Lidar · 2008
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Simulating quantum computation by contracting tensor networks
Igor L Markov and Yaoyun Shi · 2008
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Quantum computational complexity
John Watrous · 2008
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Computational complexity: a modern approach
Sanjeev Arora and Boaz Barak · 2009
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Quantum computation and quantum information
Michael A Nielsen and Isaac L Chuang · 2010
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Fourier analysis: an introduction
Elias M Stein and Rami Shakarchi · 2011
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Direct fidelity estimation from few pauli measurements
Steven T Flammia and Yi-Kai Liu · 2011
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Optimal ancilla-free clifford+ t approximation of z-rotations
Neil J Ross and Peter Selinger · 2014
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Second-order asymptotics for quantum hypothesis testing
Ke Li · 2014
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Adam: A method for stochastic optimization
Diederik P Kingma · 2014
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Quantum error correction for quantum memories
Barbara M Terhal · 2015
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Introduction to quantum gate set tomography
Daniel Greenbaum · 2015
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Quantum Phase Transitions in Transverse Field Spin Models: From Statistical Physics to Quantum Information
Amit Dutta, Gabriel Aeppli, Bikas K. Chakrabarti, Uma Divakaran, Thomas F. Rosenbaum, and Diptiman Sen · 2015
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Improved classical simulation of quantum circuits dominated by clifford gates
Sergey Bravyi and David Gosset · 2016
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Quantum supremacy through the quantum approximate optimization algorithm
Edward Farhi and Aram W Harrow · 2016
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The theory of variational hybrid quantum-classical algorithms
Jarrod R McClean, Jonathan Romero, Ryan Babbush, and Alán Aspuru-Guzik · 2016
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Deep learning
Ian Goodfellow, Yoshua Bengio, and Aaron Courville · 2016
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Neural decoder for topological codes
Giacomo Torlai and Roger G Melko · 2017
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Guest column: A survey of quantum learning theory
Srinivasan Arunachalam and Ronald de Wolf · 2017
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Geometry of quantum states: an introduction to quantum entanglement
Ingemar Bengtsson and Karol Życzkowski · 2017
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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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Shadow tomography of quantum states
Scott Aaronson · 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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Neural-network quantum state tomography
Giacomo Torlai, Guglielmo Mazzola, Juan Carrasquilla, Matthias Troyer, Roger Melko, and Giuseppe Carleo · 2018
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Constructing exact representations of quantum many-body systems with deep neural networks
Giuseppe Carleo, Yusuke Nomura, and Masatoshi Imada · 2018
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Computation of molecular spectra on a quantum processor with an error-resilient algorithm
James I Colless, Vinay V Ramasesh, Dar Dahlen, Machiel S Blok, Mollie E Kimchi-Schwartz, Jarrod R McClean, Jonathan Carter, Wibe A de Jong, and Irfan Siddiqi · 2018
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Quantum circuit learning
Kosuke Mitarai, Makoto Negoro, Masahiro Kitagawa, and Keisuke Fujii · 2018
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Foundations of machine learning
Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar · 2018
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A flexible high-performance simulator for verifying and benchmarking quantum circuits implemented on real hardware
Benjamin Villalonga, Sergio Boixo, Bron Nelson, Christopher Henze, Eleanor Rieffel, Rupak Biswas, and Salvatore Mandrà · 2019
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Simulation of quantum circuits by low-rank stabilizer decompositions
Sergey Bravyi, Dan Browne, Padraic Calpin, Earl Campbell, David Gosset, and Mark Howard · 2019
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Quantum supremacy using a programmable superconducting processor
Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandao, David A Buell, et al · 2019
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Machine learning nonlocal correlations
Askery Canabarro, Samuraí Brito, and Rafael Chaves · 2019
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Reconstructing quantum states with generative models
Juan Carrasquilla, Giacomo Torlai, Roger G Melko, and Leandro Aolita · 2019
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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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Evaluating analytic gradients on quantum hardware
Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, and Nathan Killoran · 2019
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Quantum convolutional neural networks
Iris Cong, Soonwon Choi, and Mikhail D Lukin · 2019
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Quantum certification and benchmarking
Jens Eisert, Dominik Hangleiter, Nathan Walk, Ingo Roth, Damian Markham, Rhea Parekh, Ulysse Chabaud, and Elham Kashefi · 2020
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Predicting many properties of a quantum system from very few measurements
Hsin-Yuan Huang, Richard Kueng, and John Preskill · 2020
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Jonas Haferkamp, Felipe Montealegre-Mora, Markus Heinrich, Jens Eisert, David Gross, and Ingo Roth · 2020
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Machine-learning iterative calculation of entropy for physical systems
Amit Nir, Eran Sela, Roy Beck, and Yohai Bar-Sinai · 2020
Cited alongside, same era.
Precise measurement of quantum observables with neural-network estimators
Giacomo Torlai, Guglielmo Mazzola, Giuseppe Carleo, and Antonio Mezzacapo · 2020
Cited alongside, same era.
Quantum computational chemistry
Sam McArdle, Suguru Endo, Alán Aspuru-Guzik, Simon C Benjamin, and Xiao Yuan · 2020
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.
Logical quantum processor based on reconfigurable atom arrays
Dolev Bluvstein, Simon J Evered, Alexandra A Geim, Sophie H Li, Hengyun Zhou, Tom Manovitz, Sepehr Ebadi, Madelyn Cain, Marcin Kalinowski, Dominik Hangleiter, et al · 2023
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Learning quantum systems
Valentin Gebhart, Raffaele Santagati, Antonio Andrea Gentile, Erik M Gauger, David Craig, Natalia Ares, Leonardo Banchi, Florian Marquardt, Luca Pezzè, and Cristian Bonato · 2023
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Approximate autonomous quantum error correction with reinforcement learning
Yexiong Zeng, Zheng-Yang Zhou, Enrico Rinaldi, Clemens Gneiting, and Franco Nori · 2023
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Neural-network decoders for measurement induced phase transitions
Hossein Dehghani, Ali Lavasani, Mohammad Hafezi, and Michael J Gullans · 2023
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Realizing a deep reinforcement learning agent for real-time quantum feedback
Kevin Reuer, Jonas Landgraf, Thomas Fösel, James O’Sullivan, Liberto Beltrán, Abdulkadir Akin, Graham J Norris, Ants Remm, Michael Kerschbaum, Jean-Claude Besse, et al · 2023
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Matrix product states and projected entangled pair states: Concepts, symmetries, theorems
J Ignacio Cirac, David Perez-Garcia, Norbert Schuch, and Frank Verstraete · 2021
Cited alongside, same era.
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
Cited alongside, same era.
Absence of barren plateaus in quantum convolutional neural networks
Arthur Pesah, Marco Cerezo, Samson Wang, Tyler Volkoff, Andrew T Sornborger, and Patrick J Coles · 2021
Cited alongside, same era.
Toward trainability of deep quantum neural networks
Kaining Zhang, Min-Hsiu Hsieh, Liu Liu, and Dacheng Tao · 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.
Entanglement-induced barren plateaus
Carlos Ortiz Marrero, Mária Kieferová, and Nathan Wiebe · 2021
Cited alongside, same era.
Efficient estimation of pauli observables by derandomization
Hsin-Yuan Huang, Richard Kueng, and John Preskill · 2021
Cited alongside, same era.
Deep learning of quantum entanglement from incomplete measurements
Dominik Koutnỳ, Laia Ginés, Magdalena Moczała-Dusanowska, Sven Höfling, Christian Schneider, Ana Predojević, and Miroslav Ježek · 2023
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The power and limitations of learning quantum dynamics incoherently
Sofiene Jerbi, Joe Gibbs, Manuel S Rudolph, Matthias C Caro, Patrick J Coles, Hsin-Yuan Huang, and Zoë Holmes · 2023
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A survey on the complexity of learning quantum states
Anurag Anshu and Srinivasan Arunachalam · 2023
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Statistical complexity of quantum learning
Leonardo Banchi, Jason Luke Pereira, Sharu Theresa Jose, and Osvaldo Simeone · 2023
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Recent advances for quantum neural networks in generative learning
Jinkai Tian, Xiaoyu Sun, Yuxuan Du, Shanshan Zhao, Qing Liu, Kaining Zhang, Wei Yi, Wanrong Huang, Chaoyue Wang, Xingyao Wu, et al · 2023
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Symmetric pruning in quantum neural networks
Xinbiao Wang, Junyu Liu, Tongliang Liu, Yong Luo, Yuxuan Du, and Dacheng Tao · 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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Synergistic pretraining of parametrized quantum circuits via tensor networks
Manuel S Rudolph, Jacob Miller, Danial Motlagh, Jing Chen, Atithi Acharya, and Alejandro Perdomo-Ortiz · 2023
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Classical surrogates for quantum learning models
Franz J Schreiber, Jens Eisert, and Johannes Jakob Meyer · 2023
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M Cerezo, Martin Larocca, Diego García-Martín, NL Diaz, Paolo Braccia, Enrico Fontana, Manuel S Rudolph, Pablo Bermejo, Aroosa Ijaz, Supanut Thanasilp, et al · 2023
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Classical simulations of noisy variational quantum circuits
Enrico Fontana, Manuel S Rudolph, Ross Duncan, Ivan Rungger, and Cristina Cîrstoiu · 2023
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Learning to predict arbitrary quantum processes
Hsin-Yuan Huang, Sitan Chen, and John Preskill · 2023
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Potential and limitations of random fourier features for dequantizing quantum machine learning
Ryan Sweke, Erik Recio, Sofiene Jerbi, Elies Gil-Fuster, Bryce Fuller, Jens Eisert, and Johannes Jakob Meyer · 2023
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Classical surrogate simulation of quantum systems with lowesa
Manuel S Rudolph, Enrico Fontana, Zoë Holmes, and Lukasz Cincio · 2023
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Efficient learning of ground & thermal states within phases of matter
Emilio Onorati, Cambyse Rouzé, Daniel Stilck França, and James D Watson · 2023
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Provably efficient learning of phases of matter via dissipative evolutions
Emilio Onorati, Cambyse Rouzé, Daniel Stilck França, and James D Watson · 2023
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Fourier expansion in variational quantum algorithms
Nikita A. Nemkov, Evgeniy O. Kiktenko, and Aleksey K. Fedorov · 2023
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Multidimensional fourier series with quantum circuits
Berta Casas and Alba Cervera-Lierta · 2023
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Shadownet for data-centric quantum system learning
Yuxuan Du, Yibo Yang, Tongliang Liu, Zhouchen Lin, Bernard Ghanem, and Dacheng Tao · 2023
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Quantum similarity testing with convolutional neural networks
Ya-Dong Wu, Yan Zhu, Ge Bai, Yuexuan Wang, and Giulio Chiribella · 2023
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Problem-dependent power of quantum neural networks on multiclass classification
Yuxuan Du, Yibo Yang, Dacheng Tao, and Min-Hsiu Hsieh · 2023
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Performing su (d) operations and rudimentary algorithms in a superconducting transmon qudit for d= 3 and d= 4
Pei Liu, Ruixia Wang, Jing-Ning Zhang, Yingshan Zhang, Xiaoxia Cai, Huikai Xu, Zhiyuan Li, Jiaxiu Han, Xuegang Li, Guangming Xue, et al · 2023
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Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance
Tomislav Begušić, Johnnie Gray, and Garnet Kin-Lic Chan · 2024
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Neural-shadow quantum state tomography
Victor Wei, WA Coish, Pooya Ronagh, and Christine A Muschik · 2024
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Learning quantum states and unitaries of bounded gate complexity
Haimeng Zhao, Laura Lewis, Ishaan Kannan, Yihui Quek, Hsin-Yuan Huang, and Matthias C Caro · 2024
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Dynamical simulation via quantum machine learning with provable generalization
Joe Gibbs, Zoë Holmes, Matthias C Caro, Nicholas Ezzell, Hsin-Yuan Huang, Lukasz Cincio, Andrew T Sornborger, and Patrick J Coles · 2024
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Concept learning of parameterized quantum models from limited measurements
Beng Yee Gan, Po-Wei Huang, Elies Gil-Fuster, and Patrick Rebentrost · 2024
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Minimal-clifford shadow estimation by mutually unbiased bases
Qingyue Zhang, Qing Liu, and You Zhou · 2024
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Enhanced estimation of quantum properties with common randomized measurements
Benoît Vermersch, Aniket Rath, Bharathan Sundar, Cyril Branciard, John Preskill, and Andreas Elben · 2024
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Simulating noisy variational quantum algorithms: A polynomial approach
Yuguo Shao, Fuchuan Wei, Song Cheng, and Zhengwei Liu · 2024
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Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
Yanming Che, Clemens Gneiting, and Franco Nori · 2024
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Multimodal deep representation learning for quantum cross-platform verification
Yang Qian, Yuxuan Du, Zhenliang He, Min-Hsiu Hsieh, and Dacheng Tao · 2024
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Exponential quantum advantages in learning quantum observables from classical data
Riccardo Molteni, Casper Gyurik, and Vedran Dunjko · 2024
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Equivalence of cost concentration and gradient vanishing for quantum circuits: an elementary proof in the riemannian formulation
Qiang Miao and Thomas Barthel · 2024
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Shadows of quantum machine learning
Sofiene Jerbi, Casper Gyurik, Simon C Marshall, Riccardo Molteni, and Vedran Dunjko · 2024
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Improved machine learning algorithm for predicting ground state properties
Laura Lewis, Hsin-Yuan Huang, Viet T. Tran, Sebastian Lehner, Richard Kueng, and John Preskill · 2024
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Learning shallow quantum circuits
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Neural auto-designer for enhanced quantum kernels
Cong Lei, Yuxuan Du, Peng Mi, Jun Yu, and Tongliang Liu · 2024
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Transition role of entangled data in quantum machine learning
Xinbiao Wang, Yuxuan Du, Zhuozhuo Tu, Yong Luo, Xiao Yuan, and Dacheng Tao · 2024
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Learning quantum processes and hamiltonians via the pauli transfer matrix
Matthias C Caro · 2024
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Pauli path simulations of noisy quantum circuits beyond average case
Guillermo González-García, J Ignacio Cirac, and Rahul Trivedi · 2024
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A polynomial-time classical algorithm for noisy quantum circuits
Thomas Schuster, Chao Yin, Xun Gao, and Norman Y Yao · 2024
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Short-depth qaoa circuits and quantum annealing on higher-order ising models
Elijah Pelofske, Andreas Bärtschi, and Stephan Eidenbenz · 2024
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Benchmarking digital quantum simulations above hundreds of qubits using quantum critical dynamics
Alexander Miessen, Daniel J Egger, Ivano Tavernelli, and Guglielmo Mazzola · 2024
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Understanding quantum machine learning also requires rethinking generalization
Elies Gil-Fuster, Jens Eisert, and Carlos Bravo-Prieto · 2024
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