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This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms.
Random Quantum Circuits are Approximate 2-designs
A. W. Harrow and R. A. Low · 1919
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Uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex domain
V. I. Arnold and A. L. Krylov · 1962
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On the foundations of combinatorial theory I. Theory of Möbius Functions
G.-C. Rota · 1964
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Linear time bounds for median computations
M. Blum, R. W. Floyd, V. Pratt, R. L. Rivest, and R. E. Tarjan · 1972
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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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Probability: An Introduction
G. Grimmett and D. Welsh · 1986
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Enumerative Combinatorics
R. Stanley · 1986
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Small-bias probability spaces: efficient constructions and applications
J. Naor and M. Naor · 1990
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Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states
C. H. Bennett and S. J. Wiesner · 1992
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Information is Physical
R. Landauer · 1992
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Comparison Theorems for Reversible Markov Chains
P. Diaconis and L. Saloff-Coste · 1993
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Average entropy of a subsystem
D. N. Page · 1993
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Randomness-efficient oblivious sampling
M. Bellare and J. Rompel · 1994
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Proof of Page’s conjecture on the average entropy of a subsystem
S. K. Foong and S. Kanno · 1994
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Algorithms for quantum computation: Discrete logarithms and factoring
P. W. Shor · 1994
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Optimal Extraction of Information from Finite Quantum Ensembles
S. Massar and S. Popescu · 1995
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Randomized algorithms
R. Motwani and P. Raghavan · 1995
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Simple proof of Page’s conjecture on the average entropy of a subsystem
J. Sanchez-Ruiz · 1995
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Degree of Entanglement
A. Shimony · 1995
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Logarithmic Sobolev inequalities for finite Markov chains
P. Diaconis and L. Saloff-Coste · 1996
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A Semidefinite Bound for Mixing Rates of Markov Chains
N. Kahale · 1996
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Communication Complexity
E. Kushilevitz and N. Nisan · 1996
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Fault-tolerant quantum computation
P. W. Shor · 1996
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Stabilization of Quantum Computations by Symmetrization
A. Barenco, A. Berthiaume, D. Deutsch, A. Ekert, R. Jozsa, and C. Macchiavello · 1997
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Prescription for experimental determination of the dynamics of a quantum black box
I. L. Chuang and M. A. Nielsen · 1997
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Quantum Error Correction and Orthogonal Geometry
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane · 1997
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Quantum Mechanics Helps in Searching for a Needle in a Haystack
L. Grover · 1997
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Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate
J. F. Poyatos, J. I. Cirac, and P. Zoller · 1997
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Proof verification and the hardness of approximation problems
S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy · 1998
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Quantum Error Correction Via Codes Over GF(4)
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane · 1998
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Theory of fault-tolerant quantum computation
D. Gottesman · 1998
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Representations and Invariants of the Classical Groups
R. Goodman and N. Wallach · 1998
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Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations
D. Gottesman and I. L. Chuang · 1999
Cited alongside, same era.
Private Quantum Channels
A. Ambainis, M. Mosca, A. Tapp, and R. de Wolf · 2000
Cited alongside, same era.
Sampling adsorbing staircase walks using a new Markov chain decomposition method
R.A. Martin and D. Randall · 2000
Cited alongside, same era.
Quantum Computation and Quantum Information
M. A. Nielsen and I. L. Chuang · 2000
Cited alongside, same era.
Monotones and invariants for multi-particle quantum states
H. Barnum and N. Linden · 2001
Cited alongside, same era.
Quantum Tomography for Measuring Experimentally the Matrix Elements of an Arbitrary Quantum Operation
G. M. D’Ariano and P. Lo Presti · 2001
Cited alongside, same era.
Optimal finite measurements and Gauss quadratures
S. Iblisdir and J. Roland · 2006
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Mathematical aspects of mixing times in Markov chains
R. Montenegro and P. Tetali · 2006
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Entanglement and the Foundations of Statistical Mechanics
S. Popescu, A. J. Short, and A. Winter · 2006
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Typical entanglement of stabilizer states
G. Smith and D. Leung · 2006
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The learnability of quantum states
S. Aaronson · 2007
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Quantum t-designs: t-wise independence in the quantum world
A. Ambainis and J. Emerson · 2007
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The Concentration of Measure Phenomenon
M. Ledoux · 2001
Cited alongside, same era.
Hiding Bits in Bell States
B. M. Terhal, D. P. Divincenzo, and D. W. Leung · 2001
Cited alongside, same era.
Information-disturbance tradeoff in quantum measurement on the uniform ensemble and on the mutually unbiased bases, 2002
H. Barnum · 2002
Cited alongside, same era.
Quantum Data Hiding
D. DiVincenzo, D. Leung, and B. Terhal · 2002
Cited alongside, same era.
Classical and Quantum Computation
A. Yu. Kitaev, A. H. Shen, and M. N. Vyalyi · 2002
Cited alongside, same era.
A simple formula for the average gate fidelity of a quantum dynamical operation
M. A. Nielsen · 2002
Cited alongside, same era.
A. Ben-Aroya and A. Ta-Shma · 2007
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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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Evenly distributed unitaries: On the structure of unitary designs
D. Gross, K. Audenaert, and J. Eisert · 2007
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Distribution of bipartite entanglement for random pure states
O. Giraud · 2007
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A decoupling approach to the quantum capacity
P. Hayden, M. Horodecki, J. Yard, and A. Winter · 2007
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Black holes as mirrors: quantum information in random subsystems
P. Hayden and J. Preskill · 2007
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Efficient Generation of Generic Entanglement
R. Oliveira, O. C. O. Dahlsten, and M. B. Plenio · 2007
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Optimal two-qubit gate for generation of random bipartite entanglement
M. Znidaric · 2007
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k-Wise Independent Random Graphs
N. Alon and A. Nussboim · 2008
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Simple Permutations Mix Even Better
A. Brodsky and S. Hoory · 2008
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D. Gross and J. Eisert · 2008
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Quantum expanders from any classical Cayley graph expander
A. W. Harrow · 2008
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Superpolynomial Speedups Based on Almost Any Quantum Circuit
S. Hallgren and A. W. Harrow · 2008
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Quantum boolean functions, 2008
A. Montanaro and T. J. Osborne · 2008
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Quantum Copy-Protection and Quantum Money
S. Aaronson · 2009
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Nonmalleable encryption of quantum information
A. Ambainis, J. Bouda, and A. Winter · 2009
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Unpublished
S. Aaronson and D. Gottesman, 2009 · 2009
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On Almost Randomizing Channels with a Short Kraus Decomposition
G. Aubrun · 2009
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Are Random Pure States Useful for Quantum Computation?
M. J. Bremner, C. Mora, and A. Winter · 2009
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Most Quantum States Are Too Entangled To Be Useful As Computational Resources
D. Gross, S. T. Flammia, and J. Eisert · 2009
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Classical and Quantum Tensor Product Expanders
M. B. Hastings and A. W. Harrow · 2009
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Efficient Quantum Tensor Product Expanders and k k -Designs
A. W. Harrow and R. A. Low · 2009
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Derandomized Constructions of k-Wise (Almost) Independent Permutations
E. Kaplan, M. Naor, and O. Reingold · 2009
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Large Deviation Bounds for k-designs
R. A. Low · 2009
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Learning and Testing Algorithms for the Clifford Group
R. A. Low · 2009
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Y. Sekino and L. Susskind · 2096
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