Probing the Spacetime Structure of Entanglement in Monitored Quantum Circuits with Graph Neural Networks

TL;DR

This paper demonstrates that graph neural networks can reconstruct global entanglement in monitored quantum circuits from local measurements, revealing how information about quantum correlations is organized across spacetime scales.

Contribution

It introduces a novel graph neural network approach to infer global entanglement from local data in monitored quantum circuits, controlling the spacetime region of information aggregation.

Findings

Prediction accuracy improves with larger accessible spacetime regions.

Different architectures collapse onto a universal curve when scaled by an effective spacetime measure.

Global entanglement information is organized across spacetime scales.

Abstract

Global entanglement in quantum many-body systems is inherently nonlocal, raising the question of whether it can be inferred from local observations. We investigate this problem in monitored quantum circuits, where projective measurements generate classical records distributed across spacetime. Using graph neural networks (GNNs), we represent individual quantum trajectories as directed spacetime graphs and reconstruct the half-chain entanglement entropy from local measurement data alone. Because information propagates through the network via local message passing, the architecture directly controls the spacetime region over which correlations can be aggregated. By systematically varying this accessible scale -- through network depth and hierarchical spacetime coarse-graining -- we probe how much measurement information is required to reconstruct global entanglement. We find that prediction accuracy improves as the accessible spacetime region grows and that results from different architectures collapse when expressed in terms of an effective spacetime scale combining depth and coarse-graining. These results demonstrate that the information required to reconstruct global entanglement is organized in spacetime scales and show that graph-based learning architectures provide a controlled operational framework for probing how global quantum correlations emerge from local measurement data.