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Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates.
Probability inequalities for sums of bounded random variables
Wassily Hoeffding · 1963
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Transversal numbers of uniform hypergraphs
Noga Alon · 1990
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Inverse of strictly ultrametric matrices are of Stieltjes type
Servet Martínez, Gérard Michon, and Jaime San Martín · 1994
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A linear algebra proof that the inverse of a strictly ultrametric matrix is a strictly diagonally dominant Stieltjes matrix
Reinhard Nabben and Richard S Varga · 1994
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Theory of fault-tolerant quantum computation
Daniel Gottesman · 1998
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Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations
Daniel Gottesman and Isaac L. Chuang · 1999
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Truncations of random unitary matrices
Karol Zyczkowski and Hans-Jürgen Sommers · 2000
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Quantum computation and quantum information, 2002
Michael A Nielsen and Isaac Chuang · 2002
Earlier work this paper cites.
Improved simulation of stabilizer circuits
Scott Aaronson and Daniel Gottesman · 2004
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Convex optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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Monte Carlo errors with less errors
Ulli Wolff, Alpha Collaboration, et al · 2004
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Universal quantum computation with ideal Clifford gates and noisy ancillas
Sergey Bravyi and Alexei Kitaev · 2005
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Fast simulation of stabilizer circuits using a graph-state representation
Simon Anders and Hans J Briegel · 2006
Earlier work this paper cites.
Ghz extraction yield for multipartite stabilizer states
Sergey Bravyi, David Fattal, and Daniel Gottesman · 2006
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Massively parallel quantum computer simulator
Koen De Raedt, Kristel Michielsen, Hans De Raedt, Binh Trieu, Guido Arnold, Marcus Richter, Th Lippert, H Watanabe, and N Ito · 2006
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Quantum Algorithms for Some Hidden Shift Problems
W. van Dam, S. Hallgren, and L. Ip · 2006
Earlier work this paper cites.
Simulating quantum computation by contracting tensor networks
Igor L Markov and Yaoyun Shi · 2008
Earlier work this paper cites.
Quantum algorithms for highly non-linear Boolean functions
M. Rötteler · 2010
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Classical simulation of quantum computation, the Gottesman-Knill theorem, and slightly beyond
Maarten Van Den Nest · 2010
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Catalysis and activation of magic states in fault-tolerant architectures
Earl T. Campbell · 2011
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Simulating quantum computers with probabilistic methods
Maarten Van den Nest · 2011
Cited alongside, same era.
Efficient inner-product algorithm for stabilizer states
Hector J Garcia, Igor L Markov, and Andrew W Cross · 2012
Cited alongside, same era.
Negative quasi-probability as a resource for quantum computation
Victor Veitch, Christopher Ferrie, David Gross, and Joseph Emerson · 2012
Cited alongside, same era.
Surface code implementation of block code state distillation
Austin G Fowler, Simon J Devitt, and Cody Jones · 2013
Cited alongside, same era.
Low-overhead constructions for the fault-tolerant Toffoli gate
Cody Jones · 2013
Cited alongside, same era.
A quantum approximate optimization algorithm applied to a bounded occurrence constraint problem
Quantum ground state isoperimetric inequalities for the energy spectrum of local hamiltonians
Elizabeth Crosson and John Bowen · 2017
Later among the works it cites.
Local Hamiltonians whose ground states are hard to approximate
Lior Eldar and Aram W Harrow · 2017
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David Gross, Sepehr Nezami, and Michael Walter · 2017
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0.5 petabyte simulation of a 45-qubit quantum circuit
Thomas Häner and Damian S Steiger · 2017
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Application of a resource theory for magic states to fault-tolerant quantum computing
Mark Howard and Earl Campbell · 2017
Later among the works it cites.
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Edward Farhi, Jeffrey Goldstone, and Sam Gutmann · 2014
Cited alongside, same era.
On the geometry of stabilizer states
Héctor J. García, Igor L. Markov, and Andrew W. Cross · 2014
Cited alongside, same era.
Wigner function negativity and contextuality in quantum computation on rebits
Nicolas Delfosse, Philippe Allard Guerin, Jacob Bian, and Robert Raussendorf · 2015
Cited alongside, same era.
Qubit stabilizer states are complex projective 3-designs
Richard Kueng and David Gross · 2015
Cited alongside, same era.
Estimating outcome probabilities of quantum circuits using quasiprobabilities
Hakop Pashayan, Joel J Wallman, and Stephen D Bartlett · 2015
Cited alongside, same era.
Improved classical simulation of quantum circuits dominated by Clifford gates
Sergey Bravyi and David Gosset · 2016
Cited alongside, same era.
Trading classical and quantum computational resources
Sergey Bravyi, Graeme Smith, and John A. Smolin · 2016
Cited alongside, same era.
Richard Jozsa and Sergii Strelchuk · 2017
Later among the works it cites.
Discrete Wigner formalism for qubits and noncontextuality of Clifford gates on qubit stabilizer states
Lucas Kocia and Peter Love · 2017
Later among the works it cites.
Shorter stabilizer circuits via Bruhat decomposition and quantum circuit transformations
Dmitri Maslov and Martin Roetteler · 2017
Later among the works it cites.
Efficient Z gates for quantum computing
David C McKay, Christopher J Wood, Sarah Sheldon, Jerry M Chow, and Jay M Gambetta · 2017
Later among the works it cites.
Breaking the 49-qubit barrier in the simulation of quantum circuits
Edwin Pednault, John A Gunnels, Giacomo Nannicini, Lior Horesh, Thomas Magerlein, Edgar Solomonik, and Robert Wisnieff · 2017
Later among the works it cites.
Convex geometry of quantum resource quantification
Bartosz Regula · 2017
Later among the works it cites.
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
Closest in time.
Classical simulation of intermediate-size quantum circuits
Jianxin Chen, Fang Zhang, Mingcheng Chen, Cupjin Huang, Michael Newman, and Yaoyun Shi · 2018
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qtorch: The quantum tensor contraction handler
E Schuyler Fried, Nicolas PD Sawaya, Yudong Cao, Ian D Kivlichan, Jhonathan Romero, and Alán Aspuru-Guzik · 2018
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Explicit lower bounds on strong quantum simulation
Cupjin Huang, Michael Newman, and Mario Szegedy · 2018
Closest in time.
Contextuality bounds the efficiency of classical simulation of quantum processes
Angela Karanjai, Joel J Wallman, and Stephen D Bartlett · 2018
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Quantum supremacy circuit simulation on Sunway TaihuLight
Riling Li, Bujiao Wu, Mingsheng Ying, Xiaoming Sun, and Guangwen Yang · 2018
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Post hoc verification with a single prover
Tomoyuki Morimae and Joseph F Fitzsimons · 2018
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Quantum computing in the NISQ era and beyond
John Preskill · 2018
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Qiskit: An open-source framework for quantum computing, 2019
Gadi Aleksandrowicz, Thomas Alexander, Panagiotis Barkoutsos, Luciano Bello, Yael Ben-Haim, David Bucher, Francisco Jose Cabrera-Hernández, Jorge Carballo-Franquis, Adrian Chen, Chun-Fu Chen, Jerry M. Chow, Antonio D. Córcoles-Gonzales, Abigail J. Cross, Andrew Cross, Juan Cruz-Benito, Chris Culver, Salvador De La Puente González, Enrique De La Torre, Delton Ding, Eugene Dumitrescu, Ivan Duran, Pieter Eendebak, Mark Everitt, Ismael Faro Sertage, Albert Frisch, Andreas Fuhrer, Jay Gambetta, Borja Godoy Gago, Juan Gomez-Mosquera, Donny Greenberg, Ikko Hamamura, Vojtech Havlicek, Joe Hellmers, Łukasz Herok, Hiroshi Horii, Shaohan Hu, Takashi Imamichi, Toshinari Itoko, Ali Javadi-Abhari, Naoki Kanazawa, Anton Karazeev, Kevin Krsulich, Peng Liu, Yang Luh, Yunho Maeng, Manoel Marques, Francisco Jose Martín-Fernández, Douglas T. McClure, David McKay, Srujan Meesala, Antonio Mezzacapo, Nikolaj Moll, Diego Moreda Rodríguez, Giacomo Nannicini, Paul Nation, Pauline Ollitrault, Lee James O’Riordan, Hanhee Paik, Jesús Pérez, Anna Phan, Marco Pistoia, Viktor Prutyanov, Max Reuter, Julia Rice, Abdón Rodríguez Davila, Raymond Harry Putra Rudy, Mingi Ryu, Ninad Sathaye, Chris Schnabel, Eddie Schoute, Kanav Setia, Yunong Shi, Adenilton Silva, Yukio Siraichi, Seyon Sivarajah, John A. Smolin, Mathias Soeken, Hitomi Takahashi, Ivano Tavernelli, Charles Taylor, Pete Taylour, Kenso Trabing, Matthew Treinish, Wes Turner, Desiree Vogt-Lee, Christophe Vuillot, Jonathan A. Wildstrom, Jessica Wilson, Erick Winston, Christopher Wood, Stephen Wood, Stefan Wörner, Ismail Yunus Akhalwaya, and Christa Zoufal · 2019
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