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1. Correlator convolutional neural networks as an interpretable architecture for image-like quantum matter data

   https://doi.org/10.1038/s41467-021-23952-w  

   Miles, Cole; Bohrdt, Annabelle; Wu, Ruihan; Chiu, Christie; Xu, Muqing; Ji, Geoffrey; Greiner, Markus; Weinberger, Kilian Q.; Demler, Eugene; Kim, Eun-Ah (December 2021, Nature Communications)

   null (Ed.)

   Abstract Image-like data from quantum systems promises to offer greater insight into the physics of correlated quantum matter. However, the traditional framework of condensed matter physics lacks principled approaches for analyzing such data. Machine learning models are a powerful theoretical tool for analyzing image-like data including many-body snapshots from quantum simulators. Recently, they have successfully distinguished between simulated snapshots that are indistinguishable from one and two point correlation functions. Thus far, the complexity of these models has inhibited new physical insights from such approaches. Here, we develop a set of nonlinearities for use in a neural network architecture that discovers features in the data which are directly interpretable in terms of physical observables. Applied to simulated snapshots produced by two candidate theories approximating the doped Fermi-Hubbard model, we uncover that the key distinguishing features are fourth-order spin-charge correlators. Our approach lends itself well to the construction of simple, versatile, end-to-end interpretable architectures, thus paving the way for new physical insights from machine learning studies of experimental and numerical data. 

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2. Quantum phases of Rydberg atoms on a kagome lattice

   https://doi.org/10.1073/pnas.2015785118  

   Samajdar, Rhine; Ho, Wen Wei; Pichler, Hannes; Lukin, Mikhail D.; Sachdev, Subir (January 2021, Proceedings of the National Academy of Sciences)

   null (Ed.)

   We analyze the zero-temperature phases of an array of neutral atoms on the kagome lattice, interacting via laser excitation to atomic Rydberg states. Density-matrix renormalization group calculations reveal the presence of a wide variety of complex solid phases with broken lattice symmetries. In addition, we identify a regime with dense Rydberg excitations that has a large entanglement entropy and no local order parameter associated with lattice symmetries. From a mapping to the triangular lattice quantum dimer model, and theories of quantum phase transitions out of the proximate solid phases, we argue that this regime could contain one or more phases with topological order. Our results provide the foundation for theoretical and experimental explorations of crystalline and liquid states using programmable quantum simulators based on Rydberg atom arrays. 

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3. Probing entanglement scaling across a quantum phase transition on a quantum computer

   https://doi.org/10.1038/s41467-026-75251-x  

   Miao, Qiang; Wang, Tianyi; Brown, Kenneth R; Barthel, Thomas; Cetina, Marko (December 2026, Nature Communications)

   The investigation of strongly-correlated quantum matter is difficult due to the curse of dimensionality and intricate entanglement structures. These challenges are particularly pronounced in the vicinity of continuous quantum phase transitions, where quantum fluctuations manifest across all length scales. While quantum simulators give controlled access to a number of strongly correlated systems, the study of critical phenomena has been hampered by finite-size effects arising from diverging correlation lengths. Moreover, the experimental investigation of entanglement in many-body systems has been hindered by limitations in measurement protocols. To address these challenges, we employ the multiscale entanglement renormalization ansatz (MERA) and implement a holographic scheme for subsystem tomography on a fully-connected trapped-ion quantum computer. Our method accurately represents infinite systems and long-range correlations with few qubits, facilitating the efficient extraction of observables and entanglement properties, even at criticality. We observe a quantum phase transition with spontaneous symmetry breaking and reveal the evolution of entanglement properties across the critical point. For the first time, we demonstrate log-law scaling of subsystem entanglement entropies at criticality on a digital quantum computer. This achievement highlights the potential of MERA for the investigation of strongly-correlated many-body systems on quantum computers. 

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4. Detecting thermodynamic phase transition via explainable machine learning of photoemission spectroscopy

   https://doi.org/10.1016/j.newton.2025.100066  

   Chen, Xu; Sun, Yuanjie; Hruska, Eugen; Dixit, Vivek; Yang, Jinming; He, Yu; Wang, Yao; Liu, Fang (May 2025, Newton)

   Identifying thermodynamic signatures of electronic phases, such as superconductivity, is challenging in low-dimensional materials due to strong fluctuations and low probing volume. Spectroscopic methods are often used to identify new bulk phases, but their main measurable quantity—electronic energy gaps—is no longer an effective order parameter in low-dimensional and fluctuating systems. Combining angle-resolved photoemission with a domain-adversarial neural network, we report a data-driven method to identify thermodynamic phase transitions solely based on single-particle spectra. We demonstrate 97.6% accuracy in cuprate superconductor Bi2⁢Sr2⁢CaCu2⁢O8+𝛿 with strong superconducting fluctuations. This model notably compensates for the scarcity of experimental data by leveraging virtually inexhaustible simulated data. Further, its explainability reveals the crucial role of in-gap spectral weight in detecting phase fluctuations and thermodynamic transitions. Our work pinpoints the spectroscopic signatures of fluctuating orders and enables using spectroscopy for machine-learning-assisted material discovery for low-dimensional and strong coupling systems. 

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5. Neural-network decoders for measurement induced phase transitions

   https://doi.org/10.1038/s41467-023-37902-1  

   Dehghani, Hossein; Lavasani, Ali; Hafezi, Mohammad; Gullans, Michael J. (May 2023, Nature Communications)

   Abstract Open quantum systems have been shown to host a plethora of exotic dynamical phases. Measurement-induced entanglement phase transitions in monitored quantum systems are a striking example of this phenomena. However, naive realizations of such phase transitions requires an exponential number of repetitions of the experiment which is practically unfeasible on large systems. Recently, it has been proposed that these phase transitions can be probed locally via entangling reference qubits and studying their purification dynamics. In this work, we leverage modern machine learning tools to devise a neural network decoder to determine the state of the reference qubits conditioned on the measurement outcomes. We show that the entanglement phase transition manifests itself as a stark change in the learnability of the decoder function. We study the complexity and scalability of this approach in both Clifford and Haar random circuits and discuss how it can be utilized to detect entanglement phase transitions in generic experiments. 

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