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.

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