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We prove that random quantum circuits on any geometry, including a 1D line, can form approximate unitary designs over $n$ qubits in $\log n$ depth.
On the movement of particles suspended in liquids at rest required by the molecular kinetic theory of heat
Albert Einstein · 1905
Earlier work this paper cites.
Some evolutionary stochastic processes
MS Bartlett · 1949
Earlier work this paper cites.
Random matrices in physics
Eugene P Wigner · 1967
Earlier work this paper cites.
How to generate cryptographically strong sequences of pseudorandom bits
Manuel Blum and Silvio Micali · 1984
Earlier work this paper cites.
Classical potential theory and its probabilistic counterpart
Joseph L Doob and JI Doob · 1984
Earlier work this paper cites.
Multiple-quantum dynamics in solid state nmr
Jean Baum, Michael Munowitz, Allen N Garroway, and Alex Pines · 1985
Earlier work this paper cites.
A simple unpredictable pseudo-random number generator
Lenore Blum, Manuel Blum, and Mike Shub · 1986
Earlier work this paper cites.
Generating quasi-random sequences from semi-random sources
Miklos Santha and Umesh V. Vazirani · 1986
Earlier work this paper cites.
Random number generators: good ones are hard to find
S. K. Park and Keith W. Miller · 1988
Earlier work this paper cites.
Evolutionary game theory
Jörgen W Weibull · 1997
Earlier work this paper cites.
The fourth moment method
Bonnie Berger · 1997
Earlier work this paper cites.
Evolutionary games and population dynamics
Josef Hofbauer and Karl Sigmund · 1998
Earlier work this paper cites.
A pseudorandom generator from any one-way function
Johan Håstad, Russell Impagliazzo, Leonid A Levin, and Michael Luby · 1999
Earlier work this paper cites.
The large-n limit of superconformal field theories and supergravity
Juan Maldacena · 1999
Earlier work this paper cites.
Ads/cft correspondence and symmetry breaking
Igor R Klebanov and Edward Witten · 1999
Earlier work this paper cites.
Parallel quantum computation and quantum codes
Cristopher Moore and Martin Nilsson · 2001
Earlier work this paper cites.
Pseudo-random unitary operators for quantum information processing
Joseph Emerson, Yaakov S Weinstein, Marcos Saraceno, Seth Lloyd, and David G Cory · 2003
Earlier work this paper cites.
Improved simulation of stabilizer circuits
Scott Aaronson and Daniel Gottesman · 2004
Earlier work this paper cites.
Quantum field theory of many-body systems: From the origin of sound to an origin of light and electrons
Xiao-Gang Wen · 2004
Earlier work this paper cites.
Scalable noise estimation with random unitary operators
Joseph Emerson, Robert Alicki, and Karol Życzkowski · 2005
Earlier work this paper cites.
Efficient simulation of random quantum states and operators
Christoph Dankert · 2005
Earlier work this paper cites.
Convergence conditions for random quantum circuits
Joseph Emerson, Etera Livine, and Seth Lloyd · 2005
Earlier work this paper cites.
Lieb-robinson bounds and the generation of correlations and topological quantum order
Sergey Bravyi, Matthew B Hastings, and Frank Verstraete · 2006
Earlier work this paper cites.
Black holes as mirrors: quantum information in random subsystems
Patrick Hayden and John Preskill · 2007
Earlier work this paper cites.
Evenly distributed unitaries: On the structure of unitary designs
David Gross, Koenraad Audenaert, and Jens Eisert · 2007
Earlier work this paper cites.
Computation at a distance
Samuel A Kutin, David Petrie Moulton, and Lawren M Smithline · 2007
Earlier work this paper cites.
Computational complexity: a conceptual perspective
Oded Goldreich · 2008
Earlier work this paper cites.
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
Earlier work this paper cites.
Fast scramblers
Yasuhiro Sekino and Leonard Susskind · 2008
Earlier work this paper cites.
Non-abelian anyons and topological quantum computation
Chetan Nayak, Steven H Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma · 2008
Earlier work this paper cites.
Exact and approximate unitary 2-designs and their application to fidelity estimation
Christoph Dankert, Richard Cleve, Joseph Emerson, and Etera Livine · 2009
Earlier work this paper cites.
Random quantum circuits are approximate 2-designs
Aram W Harrow and Richard A Low · 2009
Earlier work this paper cites.
On lattices, learning with errors, random linear codes, and cryptography
Oded Regev · 2009
Earlier work this paper cites.
Computational complexity: a modern approach
Sanjeev Arora and Boaz Barak · 2009
Earlier work this paper cites.
An introduction to stochastic processes with applications to biology
Linda JS Allen · 2010
Earlier work this paper cites.
Convergence rates for arbitrary statistical moments of random quantum circuits
Winton G Brown and Lorenza Viola · 2010
Earlier work this paper cites.
Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen · 2010
Earlier work this paper cites.
Topological quantum order: stability under local perturbations
Sergey Bravyi, Matthew B Hastings, and Spyridon Michalakis · 2010
Earlier work this paper cites.
Locality in quantum systems
Matthew B Hastings · 2010
Earlier work this paper cites.
The computational complexity of linear optics
Scott Aaronson and Alex Arkhipov · 2011
Earlier work this paper cites.
Identifying topological order by entanglement entropy
Hong-Chen Jiang, Zhenghan Wang, and Leon Balents · 2012
Earlier work this paper cites.
Pseudorandom functions and lattices
Abhishek Banerjee, Chris Peikert, and Alon Rosen · 2012
Earlier work this paper cites.
The church of the symmetric subspace
Aram W. Harrow · 2013
Earlier work this paper cites.
Black holes and the butterfly effect
Stephen H Shenker and Douglas Stanford · 2014
Earlier work this paper cites.
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Seth Lloyd, Masoud Mohseni, and Patrick Rebentrost · 2014
Earlier work this paper cites.
The clifford group forms a unitary 3-design
Zak Webb · 2015
Earlier work this paper cites.
Simulation and the Monte Carlo method
Reuven Y Rubinstein and Dirk P Kroese · 2016
Earlier work this paper cites.
Local random quantum circuits are approximate polynomial-designs
Fernando GSL Brandao, Aram W Harrow, and Michał Horodecki · 2016
Earlier work this paper cites.
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MR Norman · 2016
Earlier work this paper cites.
Mark Zhandry · 2016
Earlier work this paper cites.
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Brian Swingle, Gregory Bentsen, Monika Schleier-Smith, and Patrick Hayden · 2016
Earlier work this paper cites.
Interferometric approach to probing fast scrambling
Norman Y Yao, Fabian Grusdt, Brian Swingle, Mikhail D Lukin, Dan M Stamper-Kurn, Joel E Moore, and Eugene A Demler · 2016
Earlier work this paper cites.
Complexity-theoretic foundations of quantum supremacy experiments
Scott Aaronson and Lijie Chen · 2016
Earlier work this paper cites.
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Adam Nahum, Jonathan Ruhman, Sagar Vijay, and Jeongwan Haah · 2017
Earlier work this paper cites.
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Beni Yoshida and Alexei Kitaev · 2017
Earlier work this paper cites.
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Yoshifumi Nakata, Christoph Hirche, Masato Koashi, and Andreas Winter · 2017
Earlier work this paper cites.
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Xiao-Gang Wen · 2017
Earlier work this paper cites.
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Huangjun Zhu · 2017
Earlier work this paper cites.
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Soonwon Choi, Norman Y Yao, and Mikhail D Lukin · 2017
Earlier work this paper cites.
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Martin Gärttner, Justin G Bohnet, Arghavan Safavi-Naini, Michael L Wall, John J Bollinger, and Ana Maria Rey · 2017
Earlier work this paper cites.
Weingarten calculus via orthogonality relations: new applications
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Earlier work this paper cites.
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Adam Nahum, Sagar Vijay, and Jeongwan Haah · 2018
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Jarrod R McClean, Sergio Boixo, Vadim N Smelyanskiy, Ryan Babbush, and Hartmut Neven · 2018
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Ethan Lake, Shankar Balasubramanian, and Soonwon Choi · 2022
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Foundations for learning from noisy quantum experiments
Hsin-Yuan Huang, Steven T Flammia, and John Preskill · 2022
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Quantum supremacy using a programmable superconducting processor
Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandao, David A Buell, et al · 2019
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Photon-mediated spin-exchange dynamics of spin-1 atoms
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Phase transition in random circuit sampling
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Linear growth of circuit complexity from brownian dynamics
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