Sridevi Kuriyattil

Abstract:

In a fast-scrambling many-body quantum system, information is spread and entanglement is built up on a time scale 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 behavior. 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 realized in experiments with neutral-atom arrays.

Abstract:

<jats:p>We investigate the emergence of different effective geometries in stochastic Clifford circuits with sparse coupling. By changing the probability distribution for choosing two-site gates as a function of distance, we generate sparse interactions that either decay or grow with distance as a function of a single tunable parameter. Tuning this parameter reveals three distinct regimes of geometry for the spreading of correlations and growth of entanglement in the system. We observe linear geometry for short-range interactions, treelike geometry on a sparse coupling graph for long-range interactions, and an intermediate fast scrambling regime at the crossover point between the linear and treelike geometries. This transition in geometry is revealed in calculations of the subsystem entanglement entropy and tripartite mutual information. We also study emergent lightcones that govern these effective geometries by teleporting a single qubit of information from an input qubit to an output qubit. These tools help to analyze distinct geometries arising in dynamics and correlation spreading in quantum many-body systems.</jats:p>