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Uniformly random unitaries, i.e.
On a Set of Almost Deterministic k k -Independent Random Variables
A. Joffe · 1974
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A fast and simple randomized parallel algorithm for the maximal independent set problem
Noga Alon, Laslo Babai, and Alon Itai · 1986
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Coding theorem and strong converse for quantum channels
A. Winter · 1999
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The Structure of Bipartite Quantum States-Insights from Group Theory and Cryptography
Matthias Christandl · 2006
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Quantum t t -designs: t t -wise independence in the quantum world
Andris Ambainis and Joseph Emerson · 2007
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Evenly distributed unitaries: On the structure of unitary designs
David Gross, Koenraad Audenaert, and Jens Eisert · 2007
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Black holes as mirrors: quantum information in random subsystems
Patrick Hayden and John Preskill · 2007
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Symmetric groups and expander graphs
Martin Kassabov · 2007
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Randomized benchmarking of quantum gates
Emanuel Knill, Dietrich Leibfried, Rolf Reichle, Joe Britton, R Brad Blakestad, John D Jost, Chris Langer, Roee Ozeri, Signe Seidelin, and David J Wineland · 2008
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Exact and approximate unitary 2 2 -designs and their application to fidelity estimation
Christoph Dankert, Richard Cleve, Joseph Emerson, and Etera Livine · 2009
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Quantum Computation and Quantum Information: 10th Anniversary Edition
Michael A. Nielsen and Isaac L. Chuang · 2010
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Scrambling speed of random quantum circuits
Winton Brown and Omar Fawzi · 2012
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Characterizing quantum gates via randomized benchmarking
Easwar Magesan, Jay M Gambetta, and Joseph Emerson · 2012
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Secure identity-based encryption in the quantum random oracle model
Mark Zhandry · 2012
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Almost k k -wise vs. k k -wise independent permutations, and uniformity for general group actions
Noga Alon and Shachar Lovett · 2013
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Lie Groups
D. Bump · 2013
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Representation theory: a first course
William Fulton and Joe Harris · 2013
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The church of the symmetric subspace
Aram W Harrow · 2013
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Local random quantum circuits are approximate polynomial-designs
Fernando GSL Brandao, Aram W Harrow, and Michał Horodecki · 2016
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Near-linear constructions of exact unitary 2-designs
Richard Cleve, Debbie Leung, Li Liu, and Chunhao Wang · 2016
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Computational complexity and black hole horizons
Leonard Susskind · 2016
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Mark Zhandry · 2016
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Pseudorandom quantum states
Zhengfeng Ji, Yi-Kai Liu, and Fang Song · 2018
Quantum commitments and signatures without one-way functions
Tomoyuki Morimae and Takashi Yamakawa · 2022
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Prabhanjan Ananth, Aditya Gulati, Fatih Kaleoglu, and Yao-Ting Lin · 2023
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Tame automorphism groups of polynomial rings with property (t) and infinitely many alternating group quotients
Pierre-Emmanuel Caprace and Martin Kassabov · 2023
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Pseudorandom unitaries are neither real nor sparse nor noise-robust
Tobias Haug, Kishor Bharti, and Dax Enshan Koh · 2023
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Complementarity and the unitarity of the black hole S-matrix
Isaac H. Kim and John Preskill · 2023
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Uncloneable quantum encryption via oracles
Anne Broadbent and Sébastien Lord · 2020
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Andrea Coladangelo, Christian Majenz, and Alexander Poremba · 2020
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Models of quantum complexity growth
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Hadamard-free circuits expose the structure of the clifford group
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William Kretschmer · 2021
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Chuhan Lu, Minglong Qin, Fang Song, Penghui Yao, and Mingnan Zhao · 2023
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Introduction to Haar measure tools in quantum information: A beginner’s tutorial
Antonio Anna Mele · 2023
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Explicit orthogonal and unitary designs
Ryan O’Donnell, Rocco A Servedio, and Pedro Paredes · 2023
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Quantum pseudoentanglement
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Real-valued somewhat-pseudorandom unitaries
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Efficient unitary t-designs from random sums
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In preparation, 2024
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Efficient approximate unitary designs from random pauli rotations
Jeongwan Haah, Yunchao Liu, and Xinyu Tan · 2024
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Pseudorandom unitaries with non-adaptive security
Tony Metger, Alexander Poremba, Makrand Sinha, and Henry Yuen · 2024
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