# Propagation of correlations in local random quantum circuits

Propagation of correlations in local random quantum circuits We derive a dynamical bound on the propagation of correlations in local random quantum circuits—lattice spin systems where piecewise quantum operations—in space and time—occur with classical probabilities. Correlations are quantified by the Frobenius norm of the commutator of two positive operators acting on disjoint regions of a one-dimensional circular chain of length L. For a time $$t=O(L)$$ t = O ( L ) , correlations spread ballistically to spatial distances $$\mathcal {D}=t$$ D = t , growing at best, diffusively with time for any distance within that radius with extensively suppressed distance- dependent corrections. For $$t=\varOmega (L^2)$$ t = Ω ( L 2 ) , all parts of the system get almost equally correlated with exponentially suppressed distance- dependent corrections and approach the maximum amount of correlations that may be established asymptotically. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Propagation of correlations in local random quantum circuits

, Volume 15 (11) – Aug 27, 2016
16 pages

/lp/springer_journal/propagation-of-correlations-in-local-random-quantum-circuits-8M9q3B560O
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1412-y
Publisher site
See Article on Publisher Site

### Abstract

We derive a dynamical bound on the propagation of correlations in local random quantum circuits—lattice spin systems where piecewise quantum operations—in space and time—occur with classical probabilities. Correlations are quantified by the Frobenius norm of the commutator of two positive operators acting on disjoint regions of a one-dimensional circular chain of length L. For a time $$t=O(L)$$ t = O ( L ) , correlations spread ballistically to spatial distances $$\mathcal {D}=t$$ D = t , growing at best, diffusively with time for any distance within that radius with extensively suppressed distance- dependent corrections. For $$t=\varOmega (L^2)$$ t = Ω ( L 2 ) , all parts of the system get almost equally correlated with exponentially suppressed distance- dependent corrections and approach the maximum amount of correlations that may be established asymptotically.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 27, 2016

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