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Unitary $2$-designs are random unitaries simulating up to the second order statistical moments of the uniformly distributed random unitaries, often referred to as Haar random unitaries.
Linear transformations which preserve trace and positive semidefiniteness of operators
A. Jamiołkowski · 1972
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Completely positive linear maps on complex matrices
M. D. Choi · 1975
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Random Matrices
M. L. Metha · 1990
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Representations and Invariants of the Classical Groups
R. Goodman and N. R. Wallach · 1999
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Quantum data hiding
D. P. DiVincenzo, D. W. Leung, and B. M. Terhal · 2002
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Classical and Quantum Computation
A. Kitaev, A. Shen, and M. Vyalyi · 2002
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Relating Quantum Privacy and Quantum Coherence: An Operational Approach
I. Devetak and A. Winter · 2004
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Improved simulation of stabilizer circuits
S. Aaronson and D. Gottesman · 2004
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The private classical capacity and quantum capacity of a quantum channel
I. Devetak · 2005
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Scalable noise estimation with random unitary operators
J. Emerson, R. Alicki, and K. Życzkowski · 2005
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Entanglement and the foundations of statistical mechanics
S. Popescu, A. J. Short, and A. Winter · 2006
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Canonical Typicality
S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zanghí · 2006
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Black holes as mirrors: quantum information in random subsystems
P. Hayden and J. Preskill · 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 algorithm for multiqudit twirling for ensemble quantum computation
G. Tóth and J. J. García-Ripoll · 2007
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A decoupling approach to the quantum capacity
P. Hayden, M. Horodecki, A. Winter, and J. Yard · 2008
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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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Foundation of Statistical Mechanics under Experimentally Realistic Conditions
P. Reimann · 2008
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Fast scramblers
Y. Sekino and L. Susskind · 2008
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Quantum pseudorandomness from cluster-state quantum computation
W. G. Brown, Y. S. Weinstein, and L. Viola · 2008
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Parameters of pseudorandom quantum circuits
Y. S. Weinstein, W. G. Brown, and L. Viola · 2008
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The mother of all protocols : Restructuring quantum information’s family tree
A. Abeyesinghe, I. Devetak, P. Hayden, and A. Winter · 2009
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Phase-random states: Ensembles of states with fixed amplitudes and uniformly distributed phases in a fixed basis
Y. Nakata, P. S. Turner, and M. Murao · 2012
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Quantum channels and operations: Guided tour
M. M. Wolf · 2012
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Decoupling with unitary approximate two-designs
O. Szehr, F. Dupuis, M. Tomamichel, and R. Renner · 2013
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Towards the fast scrambling conjecture
N. Lashkari, D. Stanford, M. Hastings, T. Osborne, and P. Hayden · 2013
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Process verification of two-qubit quantum gates by randomized benchmarking
A. D. Córcoles, Jay M. Gambetta, Jerry M. Chow, John A. Smolin, Matthew Ware, Joel Strand, B. L. T. Plourde, and M. Steffen · 2013
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Diagonal-unitary 2-designs and their implementations by quantum circuits
Y. Nakata and M. Murao · 2013
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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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Random quantum circuits are approximate 2-designs
A. W. Harrow and R. A. Low · 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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Pseudo-randomness and learning in quantum computation
R. A. Low · 2010
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The apex of the family tree of protocols : optimal rates and resource inequalities
N. Datta and M.-H. Hsieh · 2011
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Scalable and Robust Randomized Benchmarking of Quantum Processes
E. Magesan, J. M. Gambetta, and J. Emerson · 2011
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One-shot decoupling
F. Dupuis, M. Berta, J. Wullschleger, and R. Renner · 2014
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Efficient achievability for quantum protocols using decoupling theorems
C. Hirche and C. Morgan · 2014
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Black holes and the butterfly effect
H. Shenker and D. Stanfor · 2014
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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 John M. Martinis · 2014
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Generating a state t-design by diagonal quantum circuits
Y. Nakata, M. Koashi, and M. Murao · 2014
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Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory
D. A. Roberts and D. Stanford · 2015
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Stringy effects in scrambling
S. H. Shenker and D. Stanford · 2015
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Decoupling with random diagonal unitaries
Y. Nakata, C. Hirche, C. Morgan, and A. Winter · 2015
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Near-linear constructions of exact unitary 2-designs
R. Cleve, D. Leung, L. Liu, and C. Wang · 2016
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Decoupling: A building block for quantum information theory
P. Hayden · 2017
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