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Quantum circuits -- built from local unitary gates and local measurements -- are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far-from-equilibrium.
A mathematical theory of communication
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A new axiomatic characterization of the von neumann entropy
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Renormalization of the potts model
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Entropy of an n-system from its correlation with ak-reservoir
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Random-matrix physics: spectrum and strength fluctuations
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Characterization of chaotic quantum spectra and universality of level fluctuation laws
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Shelved optical electron amplifier: Observation of quantum jumps
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Observation of quantum jumps
Th Sauter, Werner Neuhauser, Rainer Blatt, and Peter E Toschek · 1986
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Observation of quantum jumps in a single atom
Jim C Bergquist, Randall G Hulet, Wayne M Itano, and David J Wineland · 1986
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Dynamic scaling of growing interfaces
Mehran Kardar, Giorgio Parisi, and Yi-Cheng Zhang · 1986
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Quantum statistical mechanics in a closed system
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Quantum signatures of chaos
Fritz Haake · 1991
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Gapless spin-fluid ground state in a random quantum heisenberg magnet
Subir Sachdev and Jinwu Ye · 1993
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Information in black hole radiation
Don N Page · 1993
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Chaos and quantum thermalization
Mark Srednicki · 1994
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Class of quantum error-correcting codes saturating the quantum hamming bound
Daniel Gottesman · 1996
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Scaling and renormalization in statistical physics
John Cardy · 1996
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Random-matrix theory of quantum transport
Carlo WJ Beenakker · 1997
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The spectral form factor is not self-averaging
RE Prange · 1997
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The quantum-jump approach to dissipative dynamics in quantum optics
Martin B Plenio and Peter L Knight · 1998
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The Heisenberg Representation of Quantum Computers
Daniel Gottesman · 1998
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Random graphs
Béla Bollobás · 1998
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Quantum computation and quantum information, 2000
Michael A Nielson and Isaac L Chuang · 2000
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Quantum to classical phase transition in noisy quantum computers
Dorit Aharonov · 2000
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Fault-tolerant quantum computation by anyons
A Yu Kitaev · 2003
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Quantum noise: a handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics
Crispin Gardiner, Peter Zoller, and Peter Zoller · 2004
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Random matrices
Madan Lal Mehta · 2004
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Improved simulation of stabilizer circuits
Scott Aaronson and Daniel Gottesman · 2004
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Multipartite entanglement detection in bosons
C Moura Alves and D Jaksch · 2004
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Evolution of entanglement entropy in one-dimensional systems
Pasquale Calabrese and John Cardy · 2005
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Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group
Benoît Collins and Piotr Śniady · 2006
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Holographic derivation of entanglement entropy from the anti–de sitter space/conformal field theory correspondence
Shinsei Ryu and Tadashi Takayanagi · 2006
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Topological entanglement entropy
Alexei Kitaev and John Preskill · 2006
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Detecting topological order in a ground state wave function
Michael Levin and Xiao-Gang Wen · 2006
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A quantum Newton’s cradle
Toshiya Kinoshita, Trevor Wenger, and David S. Weiss · 2006
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Black holes as mirrors: quantum information in random subsystems
Patrick Hayden and John Preskill · 2007
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A covariant holographic entanglement entropy proposal
Veronika E Hubeny, Mukund Rangamani, and Tadashi Takayanagi · 2007
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Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
Maciej Lewenstein, Anna Sanpera, Veronica Ahufinger, Bogdan Damski, Aditi Sen, and Ujjwal Sen · 2007
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Generic Entanglement Can Be Generated Efficiently
R. Oliveira, O. C. O. Dahlsten, and M. B. Plenio · 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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Matrix product state representations
D Perez-Garcia, Frank Verstraete, MM Wolf, and JI Cirac · 2007
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Evolution of entanglement entropy following a quantum quench: Analytic results for the x y chain in a transverse magnetic field
Maurizio Fagotti and Pasquale Calabrese · 2008
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Spreading of correlations and entanglement after a quench in the one-dimensional bose–hubbard model
Andreas M Läuchli and Corinna Kollath · 2008
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Thermalization and its mechanism for generic isolated quantum systems
Marcos Rigol, Vanja Dunjko, and Maxim Olshanii · 2008
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Entropy scaling and simulability by matrix product states
Norbert Schuch, Michael M Wolf, Frank Verstraete, and J Ignacio Cirac · 2008
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Fast scramblers
Yasuhiro Sekino and Leonard Susskind · 2008
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Exact convergence times for generation of random bipartite entanglement
Marko Žnidarič · 2008
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Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
Frank Verstraete, Valentin Murg, and J Ignacio Cirac · 2008
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Entanglement entropy and conformal field theory
Pasquale Calabrese and John Cardy · 2009
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Random Quantum Circuits are Approximate 2-designs
Aram W. Harrow and Richard A. Low · 2009
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Matrix product states for dynamical simulation of infinite chains
Mari-Carmen Banuls, Matthew B Hastings, Frank Verstraete, and J Ignacio Cirac · 2009
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Holographic evolution of entanglement entropy
Javier Abajo-Arrastia, Joao Aparicio, and Esperanza López · 2010
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Colloquium: Area laws for the entanglement entropy
Jens Eisert, Marcus Cramer, and Martin B Plenio · 2010
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Entanglement entropy and the fermi surface
Brian Swingle · 2010
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A pedestrian’s view on interacting particle systems, kpz universality and random matrices
Thomas Kriecherbauer and Joachim Krug · 2010
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Thermodynamics of quantum jump trajectories
Juan P Garrahan and Igor Lesanovsky · 2010
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Universal digital quantum simulation with trapped ions
Ben P Lanyon, Cornelius Hempel, Daniel Nigg, Markus Müller, Rene Gerritsma, F Zähringer, Philipp Schindler, Julio T Barreiro, Markus Rambach, Gerhard Kirchmair, et al · 2011
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Field theory of non-equilibrium systems
Alex Kamenev · 2011
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Statistical distribution of quantum entanglement for a random bipartite state
Celine Nadal, Satya N Majumdar, and Massimo Vergassola · 2011
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Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
Michael J Bremner, Richard Jozsa, and Dan J Shepherd · 2011
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Unbounded growth of entanglement in models of many-body localization
Jens H Bardarson, Frank Pollmann, and Joel E Moore · 2012
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Quantum simulations with trapped ions
Rainer Blatt and Christian F Roos · 2012
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Quantum entanglement in random physical states
Alioscia Hamma, Siddhartha Santra, and Paolo Zanardi · 2012
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Entanglement renormalization and holography
Brian Swingle · 2012
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Virtual parallel computing and a search algorithm using matrix product states
Claudio Chamon and Eduardo R Mucciolo · 2012
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The kardar–parisi–zhang equation and universality class
Ivan Corwin · 2012
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Measuring entanglement growth in quench dynamics of bosons in an optical lattice
AJ Daley, H Pichler, J Schachenmayer, and P Zoller · 2012
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Ballistic spreading of entanglement in a diffusive nonintegrable system
Hyungwon Kim and David A Huse · 2013
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Universal slow growth of entanglement in interacting strongly disordered systems
Maksym Serbyn, Zlatko Papić, and Dmitry A Abanin · 2013
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Time evolution of entanglement entropy from black hole interiors
Thomas Hartman and Juan Maldacena · 2013
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Towards the fast scrambling conjecture
Nima Lashkari, Douglas Stanford, Matthew Hastings, Tobias Osborne, and Patrick Hayden · 2013
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The church of the symmetric subspace
Aram W Harrow · 2013
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Localization-protected quantum order
David A. Huse, Rahul Nandkishore, Vadim Oganesyan, Arijeet Pal, and S. L. Sondhi · 2013
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Phenomenology of fully many-body-localized systems
David A Huse, Rahul Nandkishore, and Vadim Oganesyan · 2014
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Entanglement tsunami: universal scaling in holographic thermalization
Hong Liu and S Josephine Suh · 2014
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Equilibrium states of generic quantum systems subject to periodic driving
Achilleas Lazarides, Arnab Das, and Roderich Moessner · 2014
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Long-time behavior of isolated periodically driven interacting lattice systems
Luca D’Alessio and Marcos Rigol · 2014
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Quantum trajectories and open many-body quantum systems
Andrew J Daley · 2014
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Hidden correlations in the hawking radiation and thermal noise
A. Kitaev · 2014
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Local random quantum circuits: Ensemble completely positive maps and swap algebras
Paolo Zanardi · 2014
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Black holes and the butterfly effect
Stephen H Shenker and Douglas Stanford · 2014
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Multiple shocks
Stephen H Shenker and Douglas Stanford · 2014
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Lars Bonnes and Andreas M Läuchli · 2014
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Hilbert-glass transition: New universality of temperature-tuned many-body dynamical quantum criticality
David Pekker, Gil Refael, Ehud Altman, Eugene Demler, and Vadim Oganesyan · 2014
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Many-body localization and thermalization in quantum statistical mechanics
Rahul Nandkishore and David A Huse · 2015
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Entanglement scrambling in 2d conformal field theory
Curtis T Asplund, Alice Bernamonti, Federico Galli, and Thomas Hartman · 2015
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Localized shocks
Daniel A Roberts, Douglas Stanford, and Leonard Susskind · 2015
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Observation of many-body localization of interacting fermions in a quasirandom optical lattice
Michael Schreiber, Sean S Hodgman, Pranjal Bordia, Henrik P Lüschen, Mark H Fischer, Ronen Vosk, Ehud Altman, Ulrich Schneider, and Immanuel Bloch · 2015
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Stringy effects in scrambling
Stephen H Shenker and Douglas Stanford · 2015
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Periodically driven ergodic and many-body localized quantum systems
Pedro Ponte, Anushya Chandran, Z Papić, and Dmitry A Abanin · 2015
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Localized shocks
Daniel A. Roberts, Douglas Stanford, and Leonard Susskind · 2015
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A kpz cocktail-shaken, not stirred…
Timothy Halpin-Healy and Kazumasa A Takeuchi · 2015
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Semiclassical limit for the many-body localization transition
Anushya Chandran and CR Laumann · 2015
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Fate of many-body localization under periodic driving
A. Lazarides, A. Das, and R. Moessner · 2015
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Many-body localization in periodically driven systems
Pedro Ponte, Zlatko Papić, François Huveneers, and Dmitry A Abanin · 2015
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Measuring entanglement entropy in a quantum many-body system
Rajibul Islam, Ruichao Ma, Philipp M Preiss, M Eric Tai, Alexander Lukin, Matthew Rispoli, and Markus Greiner · 2015
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From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
Luca D’Alessio, Yariv Kafri, Anatoli Polkovnikov, and Marcos Rigol · 2016
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Entanglement growth and correlation spreading with variable-range interactions in spin and fermionic tunneling models
Anton S Buyskikh, Maurizio Fagotti, Johannes Schachenmayer, Fabian Essler, and Andrew J Daley · 2016
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Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
Christian Gogolin and Jens Eisert · 2016
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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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Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
Igor L Aleiner, Lara Faoro, and Lev B Ioffe · 2016
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Holographic duality from random tensor networks
Patrick Hayden, Sepehr Nezami, Xiao-Liang Qi, Nathaniel Thomas, Michael Walter, and Zhao Yang · 2016
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Superconducting qubits: Current state of play
Morten Kjaergaard, Mollie E Schwartz, Jochen Braumüller, Philip Krantz, Joel I-J Wang, Simon Gustavsson, and William D Oliver · 2020
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Entanglement membrane in chaotic many-body systems
Tianci Zhou and Adam Nahum · 2020
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Measurement-induced criticality in random quantum circuits
Chao-Ming Jian, Yi-Zhuang You, Romain Vasseur, and Andreas WW Ludwig · 2020
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Theory of the phase transition in random unitary circuits with measurements
Yimu Bao, Soonwon Choi, and Ehud Altman · 2020
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Dynamical purification phase transition induced by quantum measurements
Michael J Gullans and David A Huse · 2020
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Scalable probes of measurement-induced criticality
Michael J Gullans and David A Huse · 2020
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Daniel A. Roberts and Brian Swingle · 2016
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Spread of entanglement and causality
Horacio Casini, Hong Liu, and Márk Mezei · 2016
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A bound on chaos
Juan Maldacena, Stephen H Shenker, and Douglas Stanford · 2016
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Many-body chaos at weak coupling
Douglas Stanford · 2016
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Lieb-robinson bound and the butterfly effect in quantum field theories
Daniel A Roberts and Brian Swingle · 2016
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Universal logarithmic scrambling in many body localization
Yu Chen · 2016
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Measurement of many-body chaos using a quantum clock
Guanyu Zhu, Mohammad Hafezi, and Tarun Grover · 2016
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Emergent conformal symmetry in nonunitary random dynamics of free fermions
Xiao Chen, Yaodong Li, Matthew PA Fisher, and Andrew Lucas · 2020
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Critical properties of the measurement-induced transition in random quantum circuits
Aidan Zabalo, Michael J Gullans, Justin H Wilson, Sarang Gopalakrishnan, David A Huse, and JH Pixley · 2020
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Measurement-induced criticality in (2+ 1)-dimensional hybrid quantum circuits
Xhek Turkeshi, Rosario Fazio, and Marcello Dalmonte · 2020
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Measurement-driven phase transition within a volume-law entangled phase
Sagar Vijay · 2020
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Measurement-induced entanglement transitions in many-body localized systems
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Mean-field entanglement transitions in random tree tensor networks
Javier Lopez-Piqueres, Brayden Ware, and Romain Vasseur · 2020
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Measurement-induced steering of quantum systems
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Quantum error correction in scrambling dynamics and measurement-induced phase transition
Soonwon Choi, Yimu Bao, Xiao-Liang Qi, and Ehud Altman · 2020
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Operator L\’evy Flight: Light Cones in Chaotic Long-Range Interacting Systems
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Exploring the membrane theory of entanglement dynamics
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Localization from hilbert space shattering: From theory to physical realizations
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Ergodicity breaking arising from hilbert space fragmentation in dipole-conserving hamiltonians
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Diffusive scaling of rényi entanglement entropy
Tianci Zhou and Andreas WW Ludwig · 2020
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Anomalous diffusion in dipole-and higher-moment-conserving systems
Johannes Feldmeier, Pablo Sala, Giuseppe De Tomasi, Frank Pollmann, and Michael Knap · 2020
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Fracton hydrodynamics
Andrey Gromov, Andrew Lucas, and Rahul M Nandkishore · 2020
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Topology and broken symmetry in floquet systems
Fenner Harper, Rahul Roy, Mark S. Rudner, and S.L. Sondhi · 2020
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Statistics of the spectral form factor in the self-dual kicked ising model
Ana Flack, Bruno Bertini, and Tomaž Prosen · 2020
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Operator entanglement in local quantum circuits i: Chaotic dual-unitary circuits
Bruno Bertini, Pavel Kos, and Tomaz Prosen · 2020
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Exact dynamics in dual-unitary quantum circuits
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Planar maximally entangled states
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Measurement-induced phase transitions in quantum automaton circuits
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Nonergodic quantum dynamics from deformations of classical cellular automata
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Entanglement and dynamics of diffusion-annihilation processes with majorana defects
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Chao-Ming Jian, Bela Bauer, Anna Keselman, and Andreas WW Ludwig · 2020
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Efficient classical simulation of noisy random quantum circuits in one dimension
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Quantum many-body scars and weak breaking of ergodicity
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Quantum many-body scars and hilbert space fragmentation: A review of exact results
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Superdiffusion in spin chains
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Entanglement dynamics in hybrid quantum circuits
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Quantum simulators: Architectures and opportunities
Ehud Altman, Kenneth R Brown, Giuseppe Carleo, Lincoln D Carr, Eugene Demler, Cheng Chin, Brian DeMarco, Sophia E Economou, Mark A Eriksson, Kai-Mei C Fu, et al · 2021
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Statistical mechanics of quantum error correcting codes
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Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in landau-ginsburg theory
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Measurement-induced topological entanglement transitions in symmetric random quantum circuits
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Measurement-protected quantum phases
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Topological order and criticality in (2+ 1) d monitored random quantum circuits
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Effective theory for the measurement-induced phase transition of dirac fermions
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Measurement-induced phase transition in the monitored sachdev-ye-kitaev model
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Measurement-induced entanglement transitions in the quantum ising chain: From infinite to zero clicks
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Entanglement phase transitions in measurement-only dynamics
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Absolutely stable spatiotemporal order in noisy quantum systems
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Decoding the entanglement structure of monitored quantum circuits
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Operator backflow and the classical simulation of quantum transport
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Influence matrix approach to many-body floquet dynamics
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Many-body delocalization as symmetry breaking
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Random matrix spectral form factor of dual-unitary quantum circuits
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Local pairing of feynman histories in many-body floquet models
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Ergodic and nonergodic dual-unitary quantum circuits with arbitrary local hilbert space dimension
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Triunitary quantum circuits
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Entanglement distribution in the quantum symmetric simple exclusion process
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Multipole conservation laws and subdiffusion in any dimension
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Exact thermalization dynamics in the “rule 54” quantum cellular automaton
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Exact relaxation to gibbs and non-equilibrium steady states in the quantum cellular automaton rule 54
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Constructing quantum many-body scar hamiltonians from floquet automata
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Robust decoding in monitored dynamics of open quantum systems with z_2 symmetry
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Entanglement and charge-sharpening transitions in u (1) symmetric monitored quantum circuits
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Field theory of charge sharpening in symmetric monitored quantum circuits
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How dynamical quantum memories forget
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Postselection-free entanglement dynamics via spacetime duality
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Spacetime duality between localization transitions and measurement-induced transitions
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Many-body physics in the NISQ era: Quantum programming a discrete time crystal
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Information scrambling in quantum circuits
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Realizing topologically ordered states on a quantum processor
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Time-crystalline eigenstate order on a quantum processor
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Dynamically generated logical qubits
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Operator scaling dimensions and multifractality at measurement-induced transitions
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Measurement-induced power law negativity in an open monitored quantum circuit
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Coarse-grained entanglement and operator growth in anomalous dynamics
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Real-time correlators in chaotic quantum many-body systems
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Dissipation-assisted operator evolution method for capturing hydrodynamic transport
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Maximal entanglement velocity implies dual unitarity
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Exact emergent quantum state designs from quantum chaotic dynamics
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Construction and the ergodicity properties of dual unitary quantum circuits
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Anomalous hydrodynamics in a class of scarred frustration-free hamiltonians
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Integrability breaking in the rule 54 cellular automaton
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Fractal, logarithmic, and volume-law entangled nonthermal steady states via spacetime duality
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Entanglement dynamics of random quantum channels
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Adiabatic paths of hamiltonians, symmetries of topological order, and automorphism codes
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