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Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics.
On the Clifford collineation, transform and similarity groups. i
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On the Clifford collineation, transform and similarity groups. II
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Hausdorff measure of critical images on Banach manifolds
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Approximation by quantum circuits
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Quantum error correction and orthogonal geometry
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The Heisenberg representation of quantum computers
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Quantum computation and quantum information
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Eternal black holes in anti-de sitter
J. M. Maldacena · 2003
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Improved simulation of stabilizer circuits
S. Aaronson and D. Gottesman · 2004
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A geometric approach to quantum circuit lower bounds
M. A. Nielsen · 2005
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Optimal control, geometry, and quantum computing
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Quantum computation as geometry
M. A. Nielsen, M. R. Dowling, M. Gu, and A. C. Doherty · 2006
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Evenly distributed unitaries: on the structure of unitary designs
D. Gross, K. M. R. Audenaert, and J. Eisert · 2007
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Black holes as mirrors: quantum information in random subsystems
P. Hayden and J. Preskill · 2007
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The geometry of quantum computation
M. R. Dowling and M. A. Nielsen · 2008
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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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Semidefinite programs for completely bounded norms
J. Watrous · 2009
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Nonequilibrium dynamics of closed interacting quantum systems
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Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
D. Poulin, A. Qarry, R. Somma, and F. Verstraete · 2011
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Real algebraic geometry
J. Bochnak, M. Coste, and M.-F. Roy · 2013
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Smooth manifolds
J. M. Lee · 2013
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An algorithm for the t t -count
D. Gosset, V. Kliuchnikov, M. Mosca, and V. Russo · 2014
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Black holes and the butterfly effect
S. H. Shenker and D. Stanford · 2014
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Multiple shocks
S. H. Shenker and D. Stanford · 2014
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Complexity and shock wave geometries
D. Stanford and L. Susskind · 2014
A blueprint for demonstrating quantum supremacy with superconducting qubits
C. Neill, P. Roushan, K. Kechedzhi, S. Boixo, S. V. Isakov, V. Smelyanskiy, R. Barends, B. Burkett, Y. Chen, and Z. Chen · 2017
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Mixing properties of stochastic quantum Hamiltonians
E. Onorati, O. Buerschaper, M. Kliesch, W. Brown, A. H. Werner, and J. Eisert · 2017
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Chaos and complexity by design
D. A. Roberts and B. Yoshida · 2017
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Multi-qubit Clifford groups are unitary 3-designs
H. Zhu · 2017
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Second law of quantum complexity
A. R. Brown and L. Susskind · 2018
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Unscrambling the physics of out-of-time-order correlators
B.Swingle · 2018
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L. Susskind · 2014
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Quantum many-body systems out of equilibrium
J. Eisert, M. Friesdorf, and C. Gogolin · 2015
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Lie groups, Lie algebras, and representations: an elementary introduction
B. Hall · 2015
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The Clifford group forms a unitary 3-design
Z. Webb · 2015
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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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Operator spreading in random unitary circuits
A. Nahum, S. Vijay, and J. Haah · 2018
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Black holes and complexity classes
L. Susskind · 2018
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Quantum supremacy using a programmable superconducting processor
F. Arute et al · 2019
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Computational pseudorandomness, the wormhole growth paradox, and constraints on the AdS/CFT duality
A. Bouland, B. Fefferman, and U. Vazirani · 2019
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Models of quantum complexity growth
F. G. S. L. Brandão, W. Chemissany, N. Hunter-Jones, R. Kueng, and J. Preskill · 2019
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Unitary-projective entanglement dynamics
A. Chan, R. M. Nandkishore, M. Pretko, and G. Smith · 2019
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Complexity and entanglement for thermofield double states
S. Chapman, J. Eisert, L. Hackl, M. P. Heller, R. Jefferson, H. Marrochio, and R. C. Myers · 2019
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Unitary designs from statistical mechanics in random quantum circuits
N. Hunter-Jones · 2019
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Measurement-driven entanglement transition in hybrid quantum circuits
Y. Li, X. Chen, and M. P. A. Fisher · 2019
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Measurement-induced phase transitions in the dynamics of entanglement
B. Skinner, J. Ruhman, and A. Nahum · 2019
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J. Haferkamp and N. Hunter-Jones · 2020
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J. Haferkamp, F. Montealegre-Mora, M. Heinrich, J. Eisert, D. Gross, and I. Roth · 2020
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Entangling power and quantum circuit complexity
J. Eisert · 2021
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Resource theory of quantum uncomplexity
N. Yunger Halpern, N. B. T. Kothakonda, J. Haferkamp, A. Munson, J. Eisert, and P. Faist · 2021
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