Attention to quantum complexity: learning phases of monitored quantum dynamics

The rapid advancement of quantum hardware has introduced opportunities to study complex quantum systems while posing significant challenges in characterizing their behavior under limited and noisy data. In this talk, I will present Quantum Attention Network (QuAN) [1], a machine-learning framework that leverages attention mechanisms from large language models to tackle these challenges. Combined with a novel parameter-efficient mini-set self-attention block (MSSAB) while treating quantum measurement snapshots as tokens and ensuring permutation invariance, QuAN accesses high-order moments of bitstring distributions while prioritizing less noisy data. QuAN has demonstrated its versatility across diverse applications, including tracking entanglement scaling in the driven hard-core Bose-Hubbard model, mapping the growth of quantum complexity in deep random circuits, and constructing phase diagram for the mixed-state toric code. A key focus of my talk involves using QuAN to study measurement-induced phase transitions (MIPT), which is the transition in the entanglement scaling when subjected to mid-circuit measurement during entangling evolution. Observing MIPTs typically requires computationally intensive and non-scalable post-selection due to the probabilistic nature of measurements. QuAN overcomes this limitation with a post-selection-free approach, predicting phase boundaries that align with exact results, requiring only a small number of samples readily accessible with current experimental platforms. This work highlights QuAN's transformative potential in assisting quantum hardware, paving the way for scalable quantum system characterization.