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The representation theory of the Clifford group is playing an increasingly prominent role in quantum information theory, including in such diverse use cases as the construction of protocols for quantum system certification, quantum simulation, and quantum cryptography.
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Edgar H Brown Jr · 1972
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Roger Howe · 1989
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Jay A. Wood · 1993
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Brown-Kervaire invariants
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Bernhard Runge · 1996
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The invariants of the Clifford groups
Gabriele Nebe, Eric M. Rains, and Neil JA Sloane · 2001
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Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces
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The probabilistic method
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Stabilizer states and Clifford operations for systems of arbitrary dimensions and modular arithmetic
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Self-dual codes and invariant theory
Gabriele Nebe, Eric M Rains, and Neil James Alexander Sloane · 2006
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Hudson’s theorem for finite-dimensional quantum systems
David Gross · 2006
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The finite simple groups
Robert Wilson · 2009
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Introduction to quadratic forms
Onorato Timothy O’Meara · 2013
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An ideal characterization of the Clifford operators
JM Farinholt · 2014
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Qubit stabilizer states are complex projective 3-designs, 2015
Richard Kueng and David Gross · 2015
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Wigner function negativity and contextuality in quantum computation on rebits
Nicolas Delfosse, Philippe Allard Guerin, Jacob Bian, and Robert Raussendorf · 2015
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Distinguishing quantum states using clifford orbits
Richard Kueng, Huangjun Zhu, and David Gross · 2016
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Multiqubit randomized benchmarking using few samples
Jonas Helsen, Joel J Wallman, Steven T Flammia, and Stephanie Wehner · 2019
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Guaranteed recovery of quantum processes from few measurements
Martin Kliesch, Richard Kueng, Jens Eisert, and David Gross · 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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Probabilistic exact universal quantum circuits for transforming unitary operations
Marco Túlio Quintino, Qingxiuxiong Dong, Atsushi Shimbo, Akihito Soeda, and Mio Murao · 2019
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Complex conjugation supermap of unitary quantum maps and its universal implementation protocol
Jisho Miyazaki, Akihito Soeda, and Mio Murao · 2019
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Richard Kueng, Huangjun Zhu, and David Gross · 2016
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The Clifford group fails gracefully to be a unitary 4-design, 2016
Huangjun Zhu, Richard Kueng, Markus Grassl, and David Gross · 2016
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The Clifford group forms a unitary 3-design
Zak Webb · 2016
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Permutation symmetry determines the discrete wigner function
Huangjun Zhu · 2016
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Phase retrieval using unitary 2-designs
Shelby Kimmel and Yi-Kai Liu · 2017
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Multiqubit Clifford groups are unitary 3-designs
Huangjun Zhu · 2017
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Small representations of finite classical groups
Shamgar Gurevich and Roger Howe · 2017
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Jonas Haferkamp, Felipe Montealegre-Mora, Markus Heinrich, Jens Eisert, David Gross, and Ingo Roth · 2020
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Unitary t-groups
Eiichi Bannai, Gabriel Navarro, Noelia Rizo, and Pham Huu Tiep · 2020
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Multipartite entanglement in stabilizer tensor networks
Sepehr Nezami and Michael Walter · 2020
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Schur–weyl duality for the clifford group with applications: Property testing, a robust hudson theorem, and de finetti representations
David Gross, Sepehr Nezami, and Michael Walter · 2021
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Rank-deficient representations in the theta correspondence over finite fields arise from quantum codes
Felipe Montealegre-Mora and David Gross · 2021
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The complex conjugate invariants of clifford groups
Eiichi Bannai, Manabu Oura, and Da Zhao · 2021
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Harmonic analysis on GL(n) over finite fields
Shamgar Gurevich and Roger Howe · 2021
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On stabiliser techniques and their application to simulation and certification of quantum devices
Markus Heinrich · 2021
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