Operator growth in random quantum circuits with symmetry

A. W. Harrow and R. A. Low, “Random Quantum Circuits are Approximate 2-designs,” Commun. Math. Phys

Original

1919

Earlier work this paper cites.

G. I. Taylor, “Diffusion by Continuous Movements,” Proc. London Math. Soc

1922

Earlier work this paper cites.

S. Goldstein, “On diffusion by discontinuous movements, and on the telegraph equation,” Quart. J. Mech. Appl. Math

1951

Earlier work this paper cites.

F. J. Dyson, “The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics,” J. Math. Phys

1962

Earlier work this paper cites.

E. H. Lieb and D. W. Robinson, “The finite group velocity of quantum spin systems,” Commun. Math. Phys

1972

Earlier work this paper cites.

E. Renshaw and R. Henderson, “The correlated random walk,” J. Appl. Probab

1981

Earlier work this paper cites.

Random Materials and Processes Series. North-Holland, 1994

G. H. Weiss, Aspects and applications of the random walk · 1994

Earlier work this paper cites.

A. Altland and M. R. Zirnbauer, “Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures,” Phys. Rev

1997

Earlier work this paper cites.

B. Collins, “Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability,” Int. Math. Res. Not

2003

Earlier work this paper cites.

Springer Complexity. Springer, 2004

C. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences · 2004

Earlier work this paper cites.

J. Emerson, E. Livine, and S. Lloyd, “Convergence conditions for random quantum circuits,” Phys. Rev

2005

Earlier work this paper cites.

B. Collins and P. Śniady, “Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group,” Commun. Math. Phys

2006

Earlier work this paper cites.

R. Oliveira, O. C. O. Dahlsten, and M. B. Plenio, “Generic entanglement can be generated efficiently,” Phys. Rev. Lett

2007

Earlier work this paper cites.

P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP

Original

2007

Earlier work this paper cites.

M. Žnidarič, “Exact convergence times for generation of random bipartite entanglement,” Phys. Rev

Original

2008

Cited alongside, same era.

B. Collins and M. Stolz, “Borel theorems for random matrices from the classical compact symmetric spaces,” Ann. Probab

2008

Cited alongside, same era.

B. Collins and S. Matsumoto, “On some properties of orthogonal weingarten functions,” J. Math. Phys

Original

2009

Cited alongside, same era.

W. G. Brown and L. Viola, “Convergence rates for arbitrary statistical moments of random quantum circuits,” Phys. Rev. Lett

Original

2010

Cited alongside, same era.

R. A. Low, “Pseudo-randomness and Learning in Quantum Computation,” arXiv:1006.5227 [quant-ph] . PhD Thesis, 2010

Original

I. L. Aleiner, L. Faoro, and L. B. Ioffe, “Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves,” Annals Phys

Original

2016

Later among the works it cites.

J. Maldacena, S. H. Shenker, and D. Stanford, “A bound on chaos,” JHEP

Original

2016

Later among the works it cites.

P. Hosur, X.-L. Qi, D. A. Roberts, and B. Yoshida, “Chaos in quantum channels,” JHEP

Original

2016

Later among the works it cites.

A. Nahum, J. Ruhman, S. Vijay, and J. Haah, “Quantum Entanglement Growth Under Random Unitary Dynamics,” Phys. Rev

Original

2017

Later among the works it cites.

Y. Gu, X.-L. Qi, and D. Stanford, “Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models,” JHEP