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

TL;DR

This paper identifies a dynamical transition in quantum circuits with tunable long-range interactions, marking the onset of information scrambling, characterized by a critical point and mean-field exponents, with implications for quantum information processing.

Contribution

It introduces a new dynamical transition in long-range quantum circuits and maps it onto a long-range Ising model, providing analytical and numerical insights.

Findings

Critical point in information scrambling identified

Scaling collapse of tripartite mutual information observed

Transition consistent with long-range Ising model predictions

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 $\nu = -1/(1+s_c)$, 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.