Onset of scrambling as a dynamical transition in tunable-range quantum circuits

Kuriyattil, Sridevi and Hashizume, Tomohiro and Bentsen, Gregory and Daley, Andrew J. (2023) Onset of scrambling as a dynamical transition in tunable-range quantum circuits. PRX Quantum, 4 (3). 030325. ISSN 2691-3399 (https://doi.org/10.1103/PRXQuantum.4.030325)

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Abstract

In a fast scrambling many-body quantum system, information is spread and entanglement is built up on a timescale that grows logarithmically with the system size. This is of fundamental interest in understanding the dynamics of many-body systems, as well as in efficiently producing entangled resource states and error-correcting codes. In this work, we identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity. In particular, we show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse around a critical point between two clearly defined regimes of different dynamical behaviour. We study this transition analytically in a related long-range Brownian circuit model and show how the transition can be mapped onto the statistical mechanics of a long-range Ising model in a particular region of parameter space. This mapping predicts mean-field critical exponents ν = −1/(1 + sc), which are consistent with the critical exponents extracted from Clifford circuit numerics. In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic, sparse circuits that can be realised in experiments with neutral atom arrays.

ORCID iDs

Kuriyattil, Sridevi, Hashizume, Tomohiro, Bentsen, Gregory and Daley, Andrew J. ORCID logoORCID: https://orcid.org/0000-0001-9005-7761;
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