Post-Selection-Free Decoding of Measurement-Induced Area-Law Phases via Neural Networks

TL;DR

This paper introduces a neural network-based method to classify measurement-induced quantum phases directly from raw measurement data, eliminating the need for post-selection and quantum state reconstruction.

Contribution

The authors develop a neural network architecture that classifies quantum phases from measurement outcomes, enabling experimental detection without post-selection.

Findings

Neural network accurately classifies phases from raw data.

System relaxation correlates with classifier accuracy convergence.

Method is robust across different data sizes and system scales.

Abstract

Monitored quantum circuits host a rich variety of exotic non-equilibrium phases. Among the most representative examples are measurement-induced phase transitions between distinct area-law entangled states. However, because these transitions are characterized by specific entanglement quantities such as mutual information or topological entanglement entropy that are nonlinear functionals of the density matrix, their experimental observation requires multiple identical quantum trajectories via post-selection, which becomes exponentially unfeasible for large systems. Here, we leverage modern machine learning tools to address this challenge. We devise a neural network architecture combining a convolutional neural network with an attention mechanism, and use raw measurement outcomes directly as input to classify trivial, long-range entangled, and symmetry-protected topological phases. We show that the system's relaxation to a steady-state phase manifests as a sharp convergence in the classifier's accuracy, entirely bypassing the need for quantum state reconstruction. We systematically study the performance of our network as a function of sample size, input data, spatial and temporal constraints, and system size scalability. Our results demonstrate that this approach is robust and post-selection free, offering a practical pathway for experimentally probing measurement-induced phases.