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Understanding the dynamics of large quantum systems is hindered by the curse of dimensionality.
Maximum-likelihood estimation of the density matrix
Konrad Banaszek, GM D’ariano, MGA Paris, and MF Sacchi · 1999
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Self testing quantum apparatus
Dominic Mayers and Andrew Yao · 2004
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The learnability of quantum states
Scott Aaronson · 2007
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Randomized benchmarking of quantum gates
Emanuel Knill, Dietrich Leibfried, Rolf Reichle, Joe Britton, R Brad Blakestad, John D Jost, Chris Langer, Roee Ozeri, Signe Seidelin, and David J Wineland · 2008
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Visualizing data using t-SNE
Laurens Van der Maaten and Geoffrey Hinton · 2008
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Quantum state tomography via compressed sensing
David Gross, Yi-Kai Liu, Steven T Flammia, Stephen Becker, and Jens Eisert · 2010
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Optimal, reliable estimation of quantum states
Robin Blume-Kohout · 2010
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Efficient quantum state tomography
Marcus Cramer, Martin B Plenio, Steven T Flammia, Rolando Somma, David Gross, Stephen D Bartlett, Olivier Landon-Cardinal, David Poulin, and Yi-Kai Liu · 2010
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Quantum computation and quantum information
Michael A Nielsen and Isaac L Chuang · 2010
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Deconvolutional networks
Matthew D Zeiler, Dilip Krishnan, Graham W Taylor, and Rob Fergus · 2010
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Direct fidelity estimation from few Pauli measurements
Steven T Flammia and Yi-Kai Liu · 2011
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14-qubit entanglement: Creation and coherence
Thomas Monz, Philipp Schindler, Julio T Barreiro, Michael Chwalla, Daniel Nigg, William A Coish, Maximilian Harlander, Wolfgang Hänsel, Markus Hennrich, and Rainer Blatt · 2011
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Quantum tomography via compressed sensing: Error bounds, sample complexity and efficient estimators
Steven T Flammia, David Gross, Yi-Kai Liu, and Jens Eisert · 2012
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Practical learning method for multi-scale entangled states
Olivier Landon-Cardinal and David Poulin · 2012
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Efficient measurement of quantum gate error by interleaved randomized benchmarking
Easwar Magesan, Jay M Gambetta, Blake R Johnson, Colm A Ryan, Jerry M Chow, Seth T Merkel, Marcus P Da Silva, George A Keefe, Mary B Rothwell, Thomas A Ohki, et al · 2012
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Robust online Hamiltonian learning
Christopher E Granade, Christopher Ferrie, Nathan Wiebe, and David G Cory · 2012
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Precision-guaranteed quantum tomography
Takanori Sugiyama, Peter S Turner, and Mio Murao · 2013
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Spatial pyramid pooling in deep convolutional networks for visual recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2015
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Sample-optimal tomography of quantum states
Jeongwan Haah, Aram W Harrow, Zhengfeng Ji, Xiaodi Wu, and Nengkun Yu · 2016
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Efficient quantum tomography
Ryan O’Donnell and John Wright · 2016
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A survey of quantum property testing
Ashley Montanaro and Ronald De Wolf · 2016
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Instance normalization: The missing ingredient for fast stylization
Dmitry Ulyanov, Andrea Vedaldi, and Victor Lempitsky · 2016
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Low rank matrix recovery from rank one measurements
Richard Kueng, Holger Rauhut, and Ulrich Terstiege · 2017
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Efficient tomography of a quantum many-body system
BP Lanyon, C Maier, Milan Holzäpfel, Tillmann Baumgratz, C Hempel, P Jurcevic, Ish Dhand, AS Buyskikh, AJ Daley, Marcus Cramer, et al · 2017
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Attention is all you need
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin · 2017
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Online learning of quantum states
Scott Aaronson, Xinyi Chen, Elad Hazan, Satyen Kale, and Ashwin Nayak · 2018
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Foundations of machine learning
Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar · 2018
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Shadow tomography of quantum states
Scott Aaronson · 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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Experimental machine learning of quantum states
Jun Gao, Lu-Feng Qiao, Zhi-Qiang Jiao, Yue-Chi Ma, Cheng-Qiu Hu, Ruo-Jing Ren, Ai-Lin Yang, Hao Tang, Man-Hong Yung, and Xian-Min Jin · 2018
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Separability-entanglement classifier via machine learning
Sirui Lu, Shilin Huang, Keren Li, Jun Li, Jianxin Chen, Dawei Lu, Zhengfeng Ji, Yi Shen, Duanlu Zhou, and Bei Zeng · 2018
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PennyLane: Automatic differentiation of hybrid quantum-classical computations
Ville Bergholm, Josh Izaac, Maria Schuld, Christian Gogolin, Shahnawaz Ahmed, Vishnu Ajith, M Sohaib Alam, Guillermo Alonso-Linaje, B AkashNarayanan, Ali Asadi, et al · 2018
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Quantum computing in the NISQ era and beyond
John Preskill · 2018
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Learning a local Hamiltonian from local measurements
Eyal Bairey, Itai Arad, and Netanel H Lindner · 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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Integrating neural networks with a quantum simulator for state reconstruction
Giacomo Torlai, Brian Timar, Evert PL Van Nieuwenburg, Harry Levine, Ahmed Omran, Alexander Keesling, Hannes Bernien, Markus Greiner, Vladan Vuletić, Mikhail D Lukin, et al · 2019
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Local-measurement-based quantum state tomography via neural networks
Tao Xin, Sirui Lu, Ningping Cao, Galit Anikeeva, Dawei Lu, Jun Li, Guilu Long, and Bei Zeng · 2019
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BERT: Pre-training of deep bidirectional transformers for language understanding
Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova · 2019
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Understanding and improving layer normalization
Optimizing shadow tomography with generalized measurements
H Chau Nguyen, Jan Lennart Bönsel, Jonathan Steinberg, and Otfried Gühne · 2022
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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
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Provably efficient machine learning for quantum many-body problems
Hsin-Yuan Huang, Richard Kueng, Giacomo Torlai, Victor V Albert, and John Preskill · 2022
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Logical shadow tomography: Efficient estimation of error-mitigated observables
Hong-Ye Hu, Ryan LaRose, Yi-Zhuang You, Eleanor Rieffel, and Zhihui Wang · 2022
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Avoiding barren plateaus using classical shadows
Stefan H Sack, Raimel A Medina, Alexios A Michailidis, Richard Kueng, and Maksym Serbyn · 2022
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Jingjing Xu, Xu Sun, Zhiyuan Zhang, Guangxiang Zhao, and Junyang Lin · 2019
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Machine learning and the physical sciences
Giuseppe Carleo, Ignacio Cirac, Kyle Cranmer, Laurent Daudet, Maria Schuld, Naftali Tishby, Leslie Vogt-Maranto, and Lenka Zdeborová · 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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Self-testing of quantum systems: A review
Ivan Šupić and Joseph Bowles · 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
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Cross-platform verification of intermediate scale quantum devices
Andreas Elben, Benoît Vermersch, Rick Van Bijnen, Christian Kokail, Tiff Brydges, Christine Maier, Manoj K Joshi, Rainer Blatt, Christian F Roos, and Peter Zoller · 2020
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Training variational quantum circuits with CoVaR: Covariance root finding with classical shadows
Gregory Boyd and Bálint Koczor · 2022
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Intelligent certification for quantum simulators via machine learning
Tailong Xiao, Jingzheng Huang, Hongjing Li, Jianping Fan, and Guihua Zeng · 2022
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Learning quantum states from their classical shadows
Hsin-Yuan Huang · 2022
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Measurements of quantum Hamiltonians with locally-biased classical shadows
Charles Hadfield, Sergey Bravyi, Rudy Raymond, and Antonio Mezzacapo · 2022
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Noisy intermediate-scale quantum algorithms
Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S Kottmann, Tim Menke, et al · 2022
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Recent advances for quantum classifiers
Weikang Li and Dong-Ling Deng · 2022
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Neural error mitigation of near-term quantum simulations
Elizabeth R Bennewitz, Florian Hopfmueller, Bohdan Kulchytskyy, Juan Carrasquilla, and Pooya Ronagh · 2022
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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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Learning many-body Hamiltonians with Heisenberg-limited scaling
Hsin-Yuan Huang, Yu Tong, Di Fang, and Yuan Su · 2023
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Adaptive quantum state tomography with active learning
Hannah Lange, Matjaž Kebrič, Maximilian Buser, Ulrich Schollwöck, Fabian Grusdt, and Annabelle Bohrdt · 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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Dimension-adaptive machine learning-based quantum state reconstruction
Sanjaya Lohani, Sangita Regmi, Joseph M Lukens, Ryan T Glasser, Thomas A Searles, and Brian T Kirby · 2023
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Performance analysis of multi-shot shadow estimation
You Zhou and Qing Liu · 2023
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Measurement optimization of variational quantum simulation by classical shadow and derandomization
Kouhei Nakaji, Suguru Endo, Yuichiro Matsuzaki, and Hideaki Hakoshima · 2023
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Shadow distillation: Quantum error mitigation with classical shadows for near-term quantum processors
Alireza Seif, Ze-Pei Cian, Sisi Zhou, Senrui Chen, and Liang Jiang · 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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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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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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Adaptive online learning of quantum states
Xinyi Chen, Elad Hazan, Tongyang Li, Zhou Lu, Xinzhao Wang, and Rui Yang · 2024
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Unified quantum state tomography and Hamiltonian learning: A language-translation-like approach for quantum systems
Zheng An, Jiahui Wu, Muchun Yang, DL Zhou, and Bei Zeng · 2024
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Classical shadows based on locally-entangled measurements
Matteo Ippoliti · 2024
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Quantum error mitigated classical shadows
Hamza Jnane, Jonathan Steinberg, Zhenyu Cai, H Chau Nguyen, and Bálint Koczor · 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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Shallow shadows: Expectation estimation using low-depth random Clifford circuits
Christian Bertoni, Jonas Haferkamp, Marcel Hinsche, Marios Ioannou, Jens Eisert, and Hakop Pashayan · 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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Classical shadow tomography for continuous variables quantum systems
Simon Becker, Nilanjana Datta, Ludovico Lami, and Cambyse Rouzé · 2024
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Tomography of quantum states from structured measurements via quantum-aware transformer
H Ma, Z Sun, D Dong, C Chen, and H Rabitz · 2025
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