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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.
Quantum Information Processing – Springer Journals
Published: Aug 27, 2016
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