Machine learning discovery of new phases in programmable Rydberg quantum simulator snapshots*

Machine learning has recently emerged as a promising approach for studying the complex and rich datasets produced by projective measurements of quantum simulators. In particular, data-centric approaches lend to the possibility of automatically discovering structure in the experimental dataset which may be missed by manual inspection. Here, we introduce a unsupervised-supervised hybrid machine learning approach, hybrid-correlation convolutional neural network (Hybrid-CCNN), and apply it to study experimental square-lattice Rydberg atom simulator snapshots to discover two new hidden phases. The initial unsupervised dimensionality reduction and clustering first revealed five distinct phase regions. We then refined these boundaries and identified each phase by training CCNNs with learnable spatial weighting and interpreting their learning. The characteristic spatial weightings and snippets of correlations specifically recognized in each phase captured the nature of quantum fluctuations in the striated phase and mapped out the phase space regions for two previously unknown phases, the rhombic and edge-ordered phases. Hence, we establish that machine learning approaches can enable discoveries of correlated and entangled quantum states hidden in large volumes of experimental snapshot data from finite size quantum simulators.