Data-Driven Learnability Transition of Measurement-Induced Entanglement

TL;DR

This paper introduces a neural network-based method to efficiently estimate measurement-induced entanglement in quantum systems, revealing a transition in learnability with increasing circuit complexity, and demonstrating robustness on noisy devices.

Contribution

It presents a data-driven, neural network approach to detect MIE without prior knowledge, identifying a learnability transition in quantum circuit depth and validating it experimentally.

Findings

Learnability transition occurs at a critical circuit depth.

Method requires polynomial resources for low-depth circuits.

Transition is robust to realistic noise on quantum devices.

Abstract

Measurement-induced entanglement (MIE) captures how local measurements generate long-range quantum correlations and drive dynamical phase transitions in many-body systems. Yet estimating MIE experimentally remains challenging: direct evaluation requires extensive post-selection over measurement outcomes, raising the question of whether MIE is accessible with only polynomial resources. We address this challenge by reframing MIE detection as a data-driven learning problem that assumes no prior knowledge of state preparation. Using measurement records alone, we train a neural network in a self-supervised manner to predict the uncertainty metric for MIE--the gap between upper and lower bounds of the average post-measurement bipartite entanglement. Applied to random circuits with one-dimensional all-to-all connectivity and two-dimensional nearest-neighbor coupling, our method reveals a learnability transition with increasing circuit depth: below a threshold, the uncertainty is small and decreases with polynomial measurement data and model parameters, while above it the uncertainty remains large despite increasing resources. We further verify this transition experimentally on current noisy quantum devices, demonstrating its robustness to realistic noise. These results highlight the power of data-driven approaches for learning MIE and delineate the practical limits of its classical learnability.