Tunable Geometries in Sparse Clifford Circuits

TL;DR

This paper explores how varying the probability distribution of two-site gates in sparse Clifford circuits leads to different effective geometries, affecting correlation spreading and entanglement growth.

Contribution

It introduces a tunable parameter controlling the geometry of interactions, revealing linear, treelike, and intermediate regimes in quantum circuit dynamics.

Findings

Identifies three distinct geometric regimes in correlation spreading.

Shows a transition from linear to treelike geometry with a tunable parameter.

Demonstrates the use of entanglement entropy and mutual information to characterize geometry.

Abstract

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.