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Near-term feasibility, classical hardness, and verifiability are the three requirements for demonstrating quantum advantage; most existing quantum advantage proposals achieve at most two.
Algorithms for quantum computation: discrete logarithms and factoring
Peter W Shor · 1994
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” non-identity-check” is qma-complete
Dominik Janzing, Pawel Wocjan, and Thomas Beth · 2005
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Non-identity check remains qma-complete for short circuits
Zhengfeng Ji and Xiaodi Wu · 2009
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Temporally unstructured quantum computation
Dan Shepherd and Michael J Bremner · 2009
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The computational complexity of linear optics
Scott Aaronson and Alex Arkhipov · 2011
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Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
Michael J Bremner, Richard Jozsa, and Dan J Shepherd · 2011
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Bosonsampling is far from uniform
Scott Aaronson and Alex Arkhipov · 2013
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Quantum error correction
Daniel A Lidar and Todd A Brun · 2013
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A quantum approximate optimization algorithm
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann · 2014
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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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The power of quantum fourier sampling
Bill Fefferman and Chris Umans · 2015
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Complexity-theoretic foundations of quantum supremacy experiments
Scott Aaronson and Lijie Chen · 2016
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Quantum supremacy through the quantum approximate optimization algorithm
Edward Farhi and Aram W Harrow · 2016
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Achieving quantum supremacy with sparse and noisy commuting quantum computations
Michael J Bremner, Ashley Montanaro, and Dan J Shepherd · 2017
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Quantum computational supremacy
Aram W Harrow and Ashley Montanaro · 2017
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Error mitigation for short-depth quantum circuits
Kristan Temme, Sergey Bravyi, and Jay M Gambetta · 2017
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Quantum supremacy and the complexity of random circuit sampling
Adam Bouland, Bill Fefferman, Chinmay Nirkhe, and Umesh Vazirani · 2018
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Quantum advantage with shallow circuits
Sergey Bravyi, David Gosset, and Robert König · 2018
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Characterizing quantum supremacy in near-term devices
Sergio Boixo, Sergei V Isakov, Vadim N Smelyanskiy, Ryan Babbush, Nan Ding, Zhang Jiang, Michael J Bremner, John M Martinis, and Hartmut Neven · 2018
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Simulating physics with computers
Richard P Feynman · 2018
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Anticoncentration theorems for schemes showing a quantum speedup
Dominik Hangleiter, Juan Bermejo-Vega, Martin Schwarz, and Jens Eisert · 2018
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Bqp-completeness of scattering in scalar quantum field theory
Stephen P Jordan, Hari Krovi, Keith SM Lee, and John Preskill · 2018
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Quantum computing in the nisq era and beyond
John Preskill · 2018
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Quantum supremacy using a programmable superconducting processor
Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando Brandao, David Buell, Brian Burkett, Yu Chen, Zijun Chen, Ben Chiaro, Roberto Collins, William Courtney, Andrew Dunsworth, Edward Farhi, Brooks Foxen, and John Martinis · 2019
Cited alongside, same era.
On the classical hardness of spoofing linear cross-entropy benchmarking
Scott Aaronson and Sam Gunn · 2019
Cited alongside, same era.
Forging quantum data: classically defeating an iqp-based quantum test
Gregory D Kahanamoku-Meyer · 2019
Cited alongside, same era.
Classical simulation of quantum supremacy circuits
Cupjin Huang, Fang Zhang, Michael Newman, Junjie Cai, Xun Gao, Zhengxiong Tian, Junyin Wu, Haihong Xu, Huanjun Yu, Bo Yuan, et al · 2020
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Suppressing quantum errors by scaling a surface code logical qubit
Google Quantum AI · 2023
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Evidence for the utility of quantum computing before fault tolerance
Youngseok Kim, Andrew Eddins, Sajant Anand, Ken Xuan Wei, Ewout van den Berg, Sami Rosenblatt, Hasan Nayfeh, Yantao Wu, Michael Zaletel, Kristan Temme, Abhinav Kandala, et al · 2023
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The hardness of random quantum circuits
Ramis Movassagh · 2023
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Spoofing cross-entropy measure in boson sampling
Changhun Oh, Liang Jiang, and Bill Fefferman · 2023
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Quantum volume for photonic quantum processors
Yuxuan Zhang, Daoheng Niu, Alireza Shabani, and Hassan Shapourian · 2023
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Boundaries of quantum supremacy via random circuit sampling
Alexander Zlokapa, Benjamin Villalonga, Sergio Boixo, and Daniel A Lidar · 2023
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Leo Zhou, Sheng-Tao Wang, Soonwon Choi, Hannes Pichler, and Mikhail D Lukin · 2020
Cited alongside, same era.
Quantum computational advantage using photons
Han-Sen Zhong, Hui Wang, Yu-Hao Deng, Ming-Cheng Chen, Li-Chao Peng, Yi-Han Luo, Jian Qin, Dian Wu, Xing Ding, Yi Hu, et al · 2020
Cited alongside, same era.
Models of quantum complexity growth
Fernando GSL Brandão, Wissam Chemissany, Nicholas Hunter-Jones, Richard Kueng, and John Preskill · 2021
Cited alongside, same era.
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.
Random quantum circuits transform local noise into global white noise
Alexander M Dalzell, Nicholas Hunter-Jones, and Fernando GSL Brandão · 2021
Cited alongside, same era.
Qed driven qaoa for network-flow optimization
Yuxuan Zhang, Ruizhe Zhang, and Andrew C Potter · 2021
Cited alongside, same era.
How much structure is needed for huge quantum speedups?
Scott Aaronson · 2022
Cited alongside, same era.
A polynomial-time classical algorithm for noisy random circuit sampling
Dorit Aharonov, Xun Gao, Zeph Landau, Yunchao Liu, and Umesh Vazirani · 2022
Cited alongside, same era.
Later among the works it cites.
On verifiable quantum advantage with peaked circuit sampling
Scott Aaronson and Yuxuan Zhang · 2024
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Learning high-accuracy error decoding for quantum error correction
Johannes Bausch et al · 2024
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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 · 2024
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Quantum error correction below the surface code threshold
Google Quantum AI · 2024
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Bell sampling from quantum circuits
Dominik Hangleiter and Michael J Gullans · 2024
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Fast classical simulation of harvard/quera iqp circuits
Dmitri Maslov, Sergey Bravyi, Felix Tripier, Andrii Maksymov, and Joe Latone · 2024
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Phase transitions in random circuit sampling
Alexis Morvan, Xiao Mi, Chris Quintana, et al · 2024
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Polynomial-time classical simulation of noisy iqp circuits with constant depth
Joel Rajakumar, James D Watson, and Yi-Kai Liu · 2024
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Leapfrogging sycamore: Harnessing 1432 gpus for 7 × \times faster quantum random circuit sampling
Xinhua Zhao, Cheng Chen, Pan Zhang, et al · 2024
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Breaking even with magic: demonstration of a high-fidelity logical non-clifford gate
Shival Dasu, Simon Burton, Karl Mayer, David Amaro, Justin A Gerber, Kevin Gilmore, Dan Gresh, Davide DelVento, Andrew C Potter, and David Hayes · 2025
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Peaked quantum advantage using error correction
Abhinav Deshpande, Bill Fefferman, Soumik Ghosh, Michael Gullans, and Dominik Hangleiter · 2025
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Digital quantum magnetism at the frontier of classical simulations
Reza Haghshenas, Eli Chertkov, Michael Mills, Wilhelm Kadow, Sheng-Hsuan Lin, Yi-Hsiang Chen, Chris Cade, Ido Niesen, Tomislav Begušić, Manuel S Rudolph, et al · 2025
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Beyond-classical computation in quantum simulation
Andrew D King, William Bernoudy, Thomas Boothby, et al · 2025
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Demonstrating an unconditional separation between quantum and classical information resources
William Kretschmer, Sabee Grewal, Matthew DeCross, Justin A Gerber, Kevin Gilmore, Dan Gresh, Nicholas Hunter-Jones, Karl Mayer, Brian Neyenhuis, David Hayes, et al · 2025
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Certified randomness using a trapped-ion quantum processor
Minzhao Liu, Ruslan Shaydulin, Pradeep Niroula, Matthew DeCross, Shih-Han Hung, Wen Yu Kon, Enrique Cervero-Martín, Kaushik Chakraborty, Omar Amer, Scott Aaronson, et al · 2025
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Random unitaries in extremely low depth
Thomas Schuster, Jonas Haferkamp, and Hsin-Yuan Huang · 2025
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