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arXiv:2509.18262 · Physical Review A

Training the classification capability of large-scale quantum cellular automata

Mario Boneberg, Simon Kochsiek, Gabriele Perfetto, Igor Lesanovsky

Published Jun 1, 2026• 0 citations
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Abstract

In the vicinity of a phase transition ergodicity can be broken. Here, different initial many-body configurations evolve towards one of several fixed points, which are macroscopically distinguishable through an order parameter. This mechanism enables state classification in quantum cellular automata and feed-forward 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.

DOI
10.1103/gds1-9vhy

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In the vicinity of a phase transition ergodicity can be broken. Here, different initial many-body configurations evolve towards one of several fixed points, which are macroscopically distinguishable through an order parameter. This mechanism enables state classification in quantum cellular automata and feed-forward 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 Z2\mathbb{Z}_2Z2​-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.
The power and expressivity of deep classical neural networks can be attributed to nonlinear input-output relations. Such nonlinearities are at the heart of many computational tasks, such as data classification and pattern recognition. Quantum neural networks, on the other hand, are necessarily linear as they process information via unitary operations. Here we show that effective nonlinearities can be implemented in these platforms by exploiting the relationship between information processing and many-body quantum dynamics. The crucial point is that quantum many-body systems can show emergent collective behavior in the vicinity of phase transitions, which leads to an effectively nonlinear dynamics in the thermodynamic limit. In the context of quantum neural networks, which are necessarily finite, this translates into metastability with transient nonergodic behavior. By using a quantum neural network the architecture of which is inspired by dissipative many-body quantum spin models, we show that this mechanism indeed allows one to realize nonlinear data classification, despite the underlying dynamics being local and linear. Our proof-of-principle study may pave the way for the systematic construction of quantum neural networks with emergent nonlinear properties.
Abstract Quantum entanglement becomes increasingly complex to analyze in many-body systems due to exponential growth in complexity with system size. In this work, we explore the potential of quantum machine learning (QML) to circumvent this. Specifically, we train a parameterized quantum neural network (QNN) model to detect transitions in the entanglement properties of the ground state in a multi-spin Ising model. This approach enables the classification of different entanglement states and provides deeper insights into the behavior of entanglement under multi-spin interactions. Our results demonstrate that QML can effectively simplify the classification process and overcome the complexity challenges encountered by classical algorithms.
Quantum neural networks generalize classical artificial neural networks into the quantum domain. They are formulated as parameterized quantum circuits which are optimized by measuring and minimizing a suitably chosen loss function. The core challenge in understanding, implementing and ultimately using quantum neural networks is that they represent many-body systems with an exponentially large Hilbert space, in combination with a large parameter search space. Moreover, noise -- which is inherent to any quantum measurement -- sets practical limits for the estimation of training loss. Here, we study physics-informed large-scale quantum neural networks that are trained through a finite number of noisy loss function measurements. We show that this architecture permits the construction of nontrivial decision boundaries that enable the classification of quantum states through measuring an order parameter. Our approach can directly process quantum data that is output from quantum simulators and computers and is well suited for implementation on current hardware. Moreover, owed to a close link between the neural network dynamics and the evolution of Markovian open many-body quantum systems, one may expect a certain robustness to noise, which is ubiquitous in the current NISQ era.
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