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A unitary $t$-design is a powerful tool in quantum information science and fundamental physics.
Schur polynomials do not have small formulas if the determinant doesn’t!
P. Chaugule et al · 1911
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Generalized Jacobi Polynomials as Spherical Functions of the Grassmann Manifold
A. T. James and A. G. Constantine · 1974
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Bounds for systems of lines, and Jacobi polynomials
P. Delsarte, J. M. Goethals, and J. J. Seidel · 1975
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Spherical codes and designs
P. Delsarte, J. M. Goethals, and J. J. Seidel · 1977
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Averaging sets: A generalization of mean values and spherical designs
P. D. Seymour and T. Zaslavsky · 1984
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Bounds for the number of nodes in Chebyshev type quadrature formulas
P. Rabau and B. Bajnok · 1991
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On averaging sets
G. Wagner and B. Volkmann · 1991
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Modern sphercal functions
M. Takeuchi · 1994
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Quantum data hiding
D. P. DiVincenzo, D. W. Leung, and B. M. Terhal · 2002
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J. Haferkamp et al · 2002
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Relating Quantum Privacy and Quantum Coherence: An Operational Approach
I. Devetak and A. Winter · 2004
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Small pseudo-random families of matrices: Derandomizing approximate quantum encryption
A. Ambainis and A. Smith · 2004
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Randomizing quantum states: Constructions and applications
P. Hayden, D. Leung, P. W. Shor, and A. Winter · 2004
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Lie Groups
D. Bump · 2004
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The private classical capacity and quantum capacity of a quantum channel
I. Devetak · 2005
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Quantum, classical, and total amount of correlations in a quantum state
B. Groisman, S. Popescu, and A. Winter · 2005
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Partial quantum information
M. Horodecki, J. Oppenheim, and A. Winter · 2005
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Scalable noise estimation with random unitary operators
J. Emerson, R. Alicki, and K. Życzkowski · 2005
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Random measurement bases, quantum state distinction and applications to the hidden subgroup problem
P. Sen · 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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Qubit-photon interactions in a cavity: Measurement-induced dephasing and number splitting
J. Gambetta et al · 2006
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Quantum t t -designs: t t -wise independence in the quantum world
A. Ambainis and J. Emerson · 2007
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Quantum state merging and negative information
M. Horodecki, J. Oppenheim, 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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Information leakage from quantum black holes with symmetry
Y. Nakata, E. Wakakuwa, and M. Koashi · 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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How to generate random matrices from the classical compact groups
F. Mezzadri · 2007
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Harmonic Analysis on Commutative Spaces
J. A. Wolf · 2007
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Randomized benchmarking of quantum gates
E. Knill et al · 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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Unitary designs and codes
A. Roy and A. J. Scott · 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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Random quantum circuits are approximate 2-designs
A. W. Harrow and R. A. Low · 2009
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Efficient Quantum Tensor Product Expanders and k-Designs
A. W. Harrow and R. A. Low · 2009
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A survey on spherical designs and algebraic combinatorics on spheres
E. Bannai and E. Bannai · 2009
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Explicit construction of exact unitary designs
E. Bannai, Y. Nakata, T. Okuda, and D. Zhao · 2009
Cited alongside, same era.
Symmetry, representations, and invariants
R. Goodman and N. R. Wallach · 2009
Near-linear constructions of exact unitary 2-designs
R. Cleve, D. Leung, L. Liu, and C. Wang · 2016
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Local Random Quantum Circuits are Approximate Polynomial-Designs
F. G. S. L. Brandão, A. W. Harrow, and M. Horodecki · 2016
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Comparing experiments to the fault-tolerance threshold
R. Kueng, D. M. Long, A. C. Doherty, and S. T. Flammia · 2016
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Low rank matrix recovery from rank one measurements
R. Kueng, H. Rauhut, and U. Terstiege · 2017
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Phase retrieval using unitary 2-designs
S. Kimmel and Y. Liu · 2017
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Chaos and complexity by design
D. A. Roberts and B. Yoshida · 2017
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Cited alongside, same era.
Large deviation bounds for k k -designs
R. A. Low · 2009
Cited alongside, same era.
A general framework for randomized benchmarking, 2020
J. Helsen, I. Roth, E. Onorati, A. H. Werner, and J. Eisert · 2010
Cited alongside, same era.
Bounds for codes and designs in complex subspaces
A. Roy · 2010
Cited alongside, same era.
Pseudo-randomness and learning in quantum computation
R. A. Low · 2010
Cited alongside, same era.
Reduced phase error through optimized control of a superconducting qubit
E. Lucero et al · 2010
Cited alongside, same era.
Scalable and Robust Randomized Benchmarking of Quantum Processes
E. Magesan, J. M. Gambetta, and J. Emerson · 2011
Cited alongside, same era.
Unitary 2-designs from random X- and Z-diagonal unitaries
Y. Nakata, C. Hirche, C. Morgan, and A. Winter · 2017
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Efficient Quantum Pseudorandomness with Nearly Time-Independent Hamiltonian Dynamics
Y. Nakata, C. Hirche, M. Koashi, and A. Winter · 2017
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Efficient simulation of quantum error correction under coherent error based on the nonunitary free-fermionic formalism
Y. Suzuki, K. Fujii, and M. Koashi · 2017
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Tensor-network simulations of the surface code under realistic noise
A. S. Darmawan and D. Poulin · 2017
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Efficient z gates for quantum computing
D. C. McKay, C. J. Wood, S. Sheldon, J. M. Chow, and J. M. Gambetta · 2017
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Characterizing quantum supremacy in near-term devices
S. Boixo et al · 2018
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A. Harrow and S. Mehraban · 2018
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Correcting coherent errors with surface codes
S. Bravyi, M. Englbrecht, König R., and N. Peard · 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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Quantum supremacy using a programmable superconducting processor
F Arute et al · 2019
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On the complexity and verification of quantum random circuit sampling
A. Bouland, B. Fefferman, C. Nirkhe, and U. Vazirani · 2019
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Three-qubit randomized benchmarking
David C. McKay et al · 2019
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Randomized benchmarking for individual quantum gates
E. Onorati, A. H. Werner, and J. Eisert · 2019
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Verified quantum information scrambling
K. A. Landsman et al · 2019
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On the explicit constructions of certain unitary t-designs
E. Bannai, M. Nakahara, D. Zhao, and Y. Zhu · 2019
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Statistical analysis of randomized benchmarking
R. Harper, I. Hincks, C. Ferrie, S. T. Flammia, and J. J. Wallman · 2019
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Rational designs
Z. Cui, J. Xia, and Z. Xiang · 2019
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Efficient unitarity randomized benchmarking of few-qubit clifford gates
B. Dirkse, J. Helsen, and S. Wehner · 2019
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Epsilon-nets, unitary designs and random quantum circuits
M. Oszmaniec, A. Sawicki, and M. Horodecki · 2020
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Unitary t t -groups
E. Bannai, G. Navarro, N. Rizo, and P. H. Tiep · 2020
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Explicit spherical designs
Z. Xiang · 2020
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Experimental implementation of non-clifford interleaved randomized benchmarking with a controlled- s s gate
S. Garion et al · 2021
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Information scrambling in computationally complex quantum circuits
X. Mi et al · 2021
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Correlated charge noise and relaxation errors in superconducting qubits
C. D. Wilen et al · 2021
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Characterizing noise correlation and enhancing coherence via qubit motion
J. Han et al · 2021
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Removing leakage-induced correlated errors in superconducting quantum error correction
M. McEwen et al · 2021
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Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits
Matt McEwen et al · 2021
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Scalable packaging design for large-scale superconducting quantum circuit
S. Tamate et al · 2021
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