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Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g.
Random quantum circuits are approximate 2-designs
A. Harrow and R. Low · 1919
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Beweis des ergodensatzes und des h-theorems in der neuen mechanik
J. Neumann · 1929
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The synthesis of two-terminal switching circuits
C. E. Shannon · 1949
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A fast and simple randomized parallel algorithm for the maximal independent set problem
N. Alon, L. Babai, and A. Itai · 1986
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How to construct random functions
O. Goldreich, S. Goldwasser, and S. Micali · 1986
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Quantum signatures of chaos
F. Haake · 1991
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Approximation by quantum circuits, 1995, arXiv:quant-ph/9508006
E. Knill · 1995
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The spectral gap for some spin chains with discrete symmetry breaking
B. Nachtergaele · 1996
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Quantum Computation and Quantum Information
M. A. Nielsen and I. L. Chuang · 2000
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The Theory of Open Quantum Systems
H. Breuer and F. Petruccione · 2002
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Quantum data hiding
B. M. T. David P. DiVincenzo, Debbie W. Leung · 2002
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Pseudo-random unitary operators for quantum information processing
J. Emerson, Y. S. Weinstein, M. Saraceno, S. Lloyd, and D. G. Cory · 2003
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Pseudo-random unitary operators for quantum information processing
J. Emerson, Y. S. Weinstein, M. Saraceno, S. Lloyd, and D. G. Cory · 2003
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Randomizing quantum states: Constructions and applications
P. Hayden, P. W. S. D. W. Leung, and A. J. Winter · 2004
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Simple Permutations Mix Even Better, 2004, arXiv:math.CO/0411098
S. Hoory and A. Brodsky · 2004
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Canonical typicality
S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zanghì · 2006
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Aspects of generic entanglement
P. Hayden, D. W. Leung, and A. Winter · 2006
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Random measurement bases, quantum state distinction and applications to the hidden subgroup problem
P. Sen · 2006
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The emergence of typical entanglement in two-party random processes
O. C. O. Dahlsten, R. Oliveira, and M. B. Plenio · 2007
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Black holes as mirrors: quantum information in random subsystems
P. Hayden and J. Preskill · 2007
On the convergence to equilibrium of Kac’s random walk on matrices
R. I. Oliveira · 2009
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Convergence rates for arbitrary statistical moments of random quantum circuits
W. G. Brown and L. Viola · 2010
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Pseudo-randomness and Learning in Quantum Computation
R. A. Low · 2010
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Strong and weak thermalization of infinite nonintegrable quantum systems
M. C. Bañuls, J. I. Cirac, and M. B. Hastings · 2011
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A spectral gap theorem in S U ( d ) SU(d) , 2011, arXiv:1108.6264
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Cited alongside, same era.
Efficient Generation of Generic Entanglement
R. Oliveira, O. C. O. Dahlsten, and M. B. Plenio · 2007
Cited alongside, same era.
Efficiency of producing random unitary matrices with quantum circuits
L. Arnaud and D. Braun · 2008
Cited alongside, same era.
Simple permutations mix even better
A. Brodsky and S. Hoory · 2008
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Exact convergence times for generation of random bipartite entanglement
M. Žnidarič · 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
Cited alongside, same era.
Efficient quantum tensor product expanders and k k -designs
A. Harrow and R. Low · 2009
Cited alongside, same era.
J. Bourgain and A. Gamburd · 2011
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Comment on ”random quantum circuits are approximate 2-designs”
I. Diniz and D. Jonathan · 2011
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Local random quantum circuits are approximate polynomial-designs, 2012, arXiv:1208.0692
F. G. S. L. Brandão, A. W. Harrow, and M. Horodecki · 2012
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S. Trotzky, Y.-A. Chen, A. Flesch, I. P. McCulloch, U. Schollwöck, J. Eisert, and I. Bloch · 2012
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Exponential quantum speed-ups are generic
F. G. Brandao and M. Horodecki · 2013
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Efficient algorithm for multiqudit twirling for ensemble quantum computation
P. Cwiklinski, M. Horodecki, M. Mozrzymas, L. Pankowski, and M. Studzinski · 2013
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Approximate orthogonality of permutations, 2013
A. W. Harrow · 2013
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Computational complexity and black hole horizons
L. Susskind · 2014
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Many-body localization and thermalization in quantum statistical mechanics
R. Nandkishore and D. A. Huse · 2015
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