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Randomized benchmarking provides a tool for obtaining precise quantitative estimates of the average error rate of a physical quantum channel.
Linear transformations which preserve trace and positive semidefiniteness of operators
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Representations of finite and compact groups , volume 10 of Graduate studies in mathematics
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The Heisenberg representation of quantum computers
D. Gottesman · 1999
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Finite group theory , volume 10
M. Aschbacher · 2000
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The invariants of the Clifford group
G. Nebe, E. M. Rains, and N. J. A. Sloane · 2001
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Entanglement measures under symmetry
K. G. H. Vollbrecht and R. F. Werner · 2001
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A 2 rebit gate universal for quantum computing
T. Rudolph and L. Grover · 2002
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Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
J. Dehaene and B. De Moor · 2003
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Scalable noise estimation with random unitary operators
J. Emerson, R. Alicki, and K. Zyczkowski · 2005
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Stabilizer states and Clifford operations for systems of arbitrary dimensions and modular arithmetic
E. Hostens, J. Dehaene, and B. De Moor · 2005
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Self-Dual Codes and Invariant Theory
G. Nebe, E. M. Rains, and N. J. A. Sloane · 2006
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Symmetrized characterization of noisy quantum processes
J. Emerson, M. Silva, O. Moussa, C. Ryan, M. Laforest, J. Baugh, D. G. Cory, and R. Laflamme · 2007
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Evenly distributed unitaries: On the structure of unitary designs
D. Gross, K. Audenaert, and J. Eisert · 2007
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Efficient error characterization in quantum information processing
B. Lévi, C. C. López, J. Emerson, and D. G. Cory · 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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Randomized benchmarking and process tomography for gate errors in a solid-state qubit
J. M. Chow, J. M. Gambetta, L. Tornberg, J. Koch, L. S. Bishop, A. A. Houck, B. R. Johnson, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf · 2009
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Exact and approximate unitary 2-designs and their application to fidelity estimation
C. Dankert, R. Cleve, J. Emerson, and E. Livine · 2009
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Unital quantum channels – convex structure and revivals of Birkhoff’s theorem
C. B. Mendl and M. M. Wolf · 2009
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Randomized benchmarking of single- and multi-qubit control in liquid-state NMR quantum information processing
C. A. Ryan, M. Laforest, and R. Laflamme · 2009
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Quantum state tomography via compressed sensing
D. Gross, Y. Liu, S. T. Flammia, S. Becker, and J. Eisert · 2010
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Randomized benchmarking of atomic qubits in an optical lattice
S. Olmschenk, R. Chicireanu, K. D. Nelson, and J. V. Porto · 2010
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Single-qubit-gate error below 𝟏𝟎 − 𝟒 {\mathbf{10}}^{-\mathbf{4}} in a trapped ion
K. R. Brown, A. C. Wilson, Y. Colombe, C. Ospelkaus, A. M. Meier, E. Knill, D. Leibfried, and D. J. Wineland · 2011
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Robust randomized benchmarking of quantum processes
Qubit stabilizer states are complex projective 3-designs
R. Kueng and D. Gross · 2015
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Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking
J. T. Muhonen, A. Laucht, S. Simmons, J. P. Dehollain, R. Kalra, F. E. Hudson, S. Freer, K. M. Itoh, D. N. Jamieson, J. C. McCallum, A. S. Dzurak, and A. Morello · 2015
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Randomized benchmarking of single-qubit gates in a 2D array of neutral-atom qubits
T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman · 2015
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Independent, extensible control of same-frequency superconducting qubits by selective broadcasting
S. Asaad, C. Dickel, N. K. Langford, S. Poletto, A. Bruno, M. A. Rol, D. Deurloo, and L. DiCarlo · 2016
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Scalable randomized benchmarking of non-Clifford gates
A. W. Cross, E. Magesan, L. S. Bishop, J. A. Smolin, and J. M. Gambetta · 2016
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E. Magesan, J. M. Gambetta, and J. Emerson · 2011
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Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators
S. T. Flammia, D. Gross, Y. Liu, and J. Eisert · 2012
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Randomized benchmarking of multiqubit gates
J. P. Gaebler, A. M. Meier, T. R. Tan, R. Bowler, Y. Lin, D. Hanneke, J. D. Jost, J. P. Home, E. Knill, D. Leibfried, and D. J. Wineland · 2012
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Characterization of addressability by simultaneous randomized benchmarking
J. M. Gambetta, A. D. Córcoles, S. T. Merkel, B. R. Johnson, J. A. Smolin, J. M. Chow, C. A. Ryan, C. Rigetti, S. Poletto, T. A. Ohki, M. B. Ketchen, and M. Steffen · 2012
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The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement
T. Heinosaari and M. Ziman · 2012
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Characterizing quantum gates via randomized benchmarking
E. Magesan, J. M. Gambetta, and J. Emerson · 2012
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Superconducting quantum circuits at the surface code threshold for fault tolerance
R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T. C. White, J. Mutus, A. G. Fowler, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, C. Neill, P. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, A. N. Cleland, and J. M. Martinis · 2014
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Learning multiexponential models with QInfer
C. Granade · 2016
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The Clifford group forms a unitary 3-design
Z. Webb · 2016
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The Clifford group fails gracefully to be a unitary 4-design
H. Zhu, R. Kueng, M. Grassl, and D. Gross · 2016
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QInfer: Statistical inference software for quantum applications
C. Granade, C. Ferrie, I. Hincks, S. Casagrande, T. Alexander, J. Gross, M. Kononenko, and Y. Sanders · 2017
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D. Gross, S. Nezami, and M. Walter · 2017
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Multi-qubit randomized benchmarking using few samples
J. Helsen, J. J. Wallman, S. T. Flammia, and S. Wehner · 2017
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Multiqubit Clifford groups are unitary 3-designs
H. Zhu · 2017
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Randomized benchmarking with restricted gate sets
W. G. Brown and B. Eastin · 2018
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Fault tolerance in the IBM Q Experience
R. Harper and S. Flammia · 2018
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Representations of the multi-qubit Clifford group
J. Helsen, J. J. Wallman, and S. Wehner · 2018
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Randomized benchmarking as convolution: Fourier analysis of gate dependent errors
S. T. Merkel, E. J. Pritchett, and B. H. Fong · 2018
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Randomized benchmarking with gate-dependent noise
J. J. Wallman · 2018
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Randomized benchmarking with gate-dependent noise
Joel Wallman · 2018
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