Attention to complexity I: witnessing the entanglement phase transition with attention-based neural networks

Improved experimental control in various platforms has enhanced our accessibility to quantum computers or more generally, quantum simulators. With the exciting opportunities brought by quantum simulators, it is crucial to develop systematic methods to reliably and efficiently extract information from experimental data. Adopting the philosophy of "measure first, ask questions later", we propose an attention-based neural network called quantum attention networks (QAN) to process measurement outcomes. QAN is tailored for quantum state measurement data by respecting the permutation invariance of individual snapshots and attending to high-order correlations between different snapshots. Among various experimental setups where QAN is applicable, we show that in the case of hard-core Bose-Hubbard (also known as the XY model) lattice emulation using transmon qubits, QAN can witness the entanglement phase transition and predict the phase boundaries that are consistent with those identified by expensive state tomography. Our findings show that QAN provides robust machinery to reveal physical insights from quantum experimental data at a much lower cost than conventional approaches.