Tunable Geometries in Sparse Clifford Circuits
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Mar 24, 2022
- Source ID
- 10.3390/sym14040666
Entities
People
- Andrew J Daley
- Gregory Bentsen
- Sridevi Kuriyattil
- Tomohiro Hashizume
Organizations
- Air Force Office of Scientific Research
- Engineering and Physical Sciences Research Council
- United States Department of Energy