In the vicinity of a phase transition ergodicity can be broken. Here, different initial many-body configurations evolve toward one of several fixed points, which are macroscopically distinguishable through an order parameter. This mechanism enables state classification in quantum cellular automata and feedforward quantum neural networks. We demonstrate that this capability can be efficiently learned from training data even in extremely high-dimensional state spaces. We illustrate this using a quantum cellular automaton that allows binary classification, which is closely connected to the dynamics of a ${\mathbb{Z}}_2$-symmetric Ising model with local interactions and dissipation. This approach can be generalized beyond binary classification and offers a natural framework for exploring the link between emergent many-body phenomena and the interpretation of data processing capabilities in the context of quantum machine learning.

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• Open quantum systems & decoherence
• Order parameters
• Phase transitions
• Cellular automata
• Machine learning
• Tensor network methods