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The approximate stabilizer rank of a quantum state is the minimum number of terms in any approximate decomposition of that state into stabilizer states.
Can quantum-mechanical description of physical reality be considered complete?
A. Einstein, B. Podolsky, and N. Rosen · 1935
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Two theorems on random polynomial time
Leonard Adleman · 1978
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Relative to a random oracle a, paˆ np7*ˆ co-npx with probability 1
H BENNETT CHARLES and JOHN GILL · 1981
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Simulating physics with computers
Richard P. Feynman · 1982
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The complexity of approximate counting
Larry Stockmeyer · 1983
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A lower bound on the monotone network complexity of the logical permanent mat, 1985
AA Razborov · 1985
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Lower bounds on the monotone complexity of some boolean function
Alexander Razborov · 1985
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The monotone circuit complexity of boolean functions
Noga Alon and Ravi B Boppana · 1987
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Non-deterministic exponential time has two-prover interactive protocols
László Babai, Lance Fortnow, and Carsten Lund · 1991
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Pp is as hard as the polynomial-time hierarchy
Seinosuke Toda · 1991
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Approximation by quantum circuits, 1995
E. Knill · 1995
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Good quantum error-correcting codes exist
A Robert Calderbank and Peter W Shor · 1996
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Quantum computers can search arbitrarily large databases by a single query
Lov K. Grover · 1997
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The heisenberg representation of quantum computers
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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Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Peter W Shor · 1999
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Quantum computing via measurements only, 2000
Robert Raussendorf and Hans J. Briegel · 2000
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A new proof of szemerédi’s theorem
W.T. Gowers · 2001
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Quantum factoring, discrete logarithms, and the hidden subgroup problem
R. Jozsa · 2001
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Quantum computers that can be simulated classically in polynomial time
Leslie G Valiant · 2001
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Efficient classical simulation of continuous variable quantum information processes
Stephen D Bartlett, Barry C Sanders, Samuel L Braunstein, and Kae Nemoto · 2002
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Improved simulation of stabilizer circuits
Scott Aaronson and Daniel Gottesman · 2004
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Competing provers yield improved karp–lipton collapse results
Jin-yi Cai, Venkatesan T Chakaravarthy, Lane A Hemaspaandra, and Mitsunori Ogihara · 2005
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Simulating adiabatic evolution of gapped spin systems
Tobias J Osborne · 2007
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Low-degree tests at large distances
Alex Samorodnitsky · 2007
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Randomized benchmarking of quantum gates
E. Knill, D. Leibfried, R. Reichle, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland · 2008
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Class of quantum many-body states that can be efficiently simulated
Guifré Vidal · 2008
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Efficient quantum pseudorandomness with nearly time-independent hamiltonian dynamics
Yoshifumi Nakata, Christoph Hirche, Masato Koashi, and Andreas Winter · 2017
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Trading t-gates for dirty qubits in state preparation and unitary synthesis
Guang Hao Low, Vadym Kliuchnikov, and Luke Schaeffer · 2018
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The theory of quantum information
John Watrous · 2018
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Limits on representing boolean functions by linear combinations of simple functions: thresholds, relus, and low-degree polynomials
Richard Ryan Williams · 2018
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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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Random quantum circuits are approximate 2-designs
Aram W. Harrow and Richard A. Low · 2009
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On lattices, learning with errors, random linear codes, and cryptography
Oded Regev · 2009
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Classical simulation of quantum computation, the gottesman-knill theorem, and slightly beyond
M. Van Den Nest · 2010
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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
Cited alongside, same era.
Quantum Computation and Quantum Information
Michael A. Nielsen and Isaac L. Chuang · 2012
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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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Stronger connections between circuit analysis and circuit lower bounds, via pcps of proximity
Lijie Chen and R Ryan Williams · 2019
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Higher-order fourier analysis and applications
Hamed Hatami, Pooya Hatami, Shachar Lovett, et al · 2019
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Unitary designs from statistical mechanics in random quantum circuits
Nicholas Hunter-Jones · 2019
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Quantum algorithms for quantum chemistry and quantum materials science
Bela Bauer, Sergey Bravyi, Mario Motta, and Garnet Kin-Lic Chan · 2020
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Quantum computational chemistry
Sam McArdle, Suguru Endo, Alán Aspuru-Guzik, Simon C. Benjamin, and Xiao Yuan · 2020
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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
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Quantum-inspired permanent identities
Ulysse Chabaud, Abhinav Deshpande, and Saeed Mehraban · 2022
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Random quantum circuits are approximate unitary t t -designs in depth O ( n t 5 + o ( 1 ) ) O\left(nt^{5+o(1)}\right)
Jonas Haferkamp · 2022
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Stabilizer rank and higher-order Fourier analysis
Farrokh Labib · 2022
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New techniques for bounding stabilizer rank
Benjamin Lovitz and Vincent Steffan · 2022
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Many-body quantum magic
Zi-Wen Liu and Andreas Winter · 2022
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Efficient classical simulation of random shallow 2d quantum circuits
John C Napp, Rolando L La Placa, Alexander M Dalzell, Fernando GSL Brandao, and Aram W Harrow · 2022
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Lower Bounds on Stabilizer Rank
Shir Peleg, Amir Shpilka, and Ben Lee Volk · 2022
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Approximate unitary t-designs by short random quantum circuits using nearest-neighbor and long-range gates
Aram W Harrow and Saeed Mehraban · 2023
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Efficient unitary designs with a system-size independent number of non-clifford gates
J. Haferkamp, F. Montealegre-Mora, M. Heinrich, J. Eisert, D. Gross, and I. Roth · 2023
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