Machine Learning Learns Minimal Representations Of Quantum Many-Body Physics From Tunnel-Coupled Bose Gas Snapshots

Understanding the complex behaviour of many-body quantum systems remains a central challenge in modern physics, yet extracting meaningful insights from experimental data often proves difficult due to inherent noise and limited observations. Frederik Møller from the Institute of Science and Technology Austria, Gabriel Fernández-Fernández from ICFO, and Thomas Schweigler from the Vienna Center for Quantum Science and Technology, alongside Paulin de Schoulepnikoff from the University of Innsbruck, Gorka Muñoz-Gil and colleagues, now demonstrate a novel machine learning approach to address this problem. The team developed a method using a variational autoencoder to analyse interference measurements from a quantum simulator studying tunnel-coupled one-dimensional Bose gases, effectively learning a simplified representation of the system’s underlying physics. This technique not only reveals the system’s equilibrium properties, but also uncovers previously hidden dynamics following rapid changes, such as the formation and behaviour of solitons, offering a powerful new tool for exploring both equilibrium and non-equilibrium physics in quantum simulators and beyond.

Learning System Parameters From Quantum Interference

Analog quantum simulators offer access to many-body dynamics beyond the reach of classical computation. However, extracting physical insights from experimental data often proves challenging due to measurement noise and incomplete knowledge of the underlying microscopic model. Researchers have now developed a machine learning approach, based on a variational autoencoder (VAE), to analyze interference measurements of tunnel-coupled one-dimensional Bose gases, a system that realizes the sine-Gordon quantum field theory. The team trained the VAE in an unsupervised manner, allowing it to learn a compressed, noise-reduced representation of the experimental data without requiring labelled training examples. This learned representation captures essential features of the quantum state, enabling reconstruction of key physical quantities such as the mass of the soliton, a stable, particle-like excitation within the system. By accurately inferring these quantities from noisy interference patterns, the method provides a powerful new tool for characterizing complex quantum systems and extracting fundamental physical insights.

Quantum Quench Dynamics in Bose Gases

This research investigates the dynamics and emergent phenomena in interacting quantum systems, specifically one-dimensional Bose gases and their behavior in Josephson junctions. A central theme is understanding how these systems relax to equilibrium after a disturbance, known as a quantum quench, and the role of prethermalization. Machine learning, particularly Variational Autoencoders (VAEs) and other neural network architectures, is used to discover hidden structure within quantum data, model complex dynamics, improve data analysis, and develop new methods for measuring temperature in quantum systems. Key findings include the observation and modeling of relaxation to a phase-locked state in bosonic Josephson junctions, investigation of universal rephasing dynamics after quantum quenches, and identification of emergent non-Gaussian correlations.

Variational Autoencoder Reveals Quantum Simulator Physics

Scientists have achieved a breakthrough in analyzing complex quantum simulations by employing a machine learning approach based on a variational autoencoder, or VAE. This work focuses on tunnel-coupled one-dimensional Bose gases, a system that realizes the sine-Gordon quantum field theory, and addresses the challenges of extracting meaningful data from noisy and incomplete measurements. The team developed a VAE that learns a minimal latent representation, effectively compressing the data into a smaller set of key parameters, which strongly correlates with the equilibrium control parameter of the system. Experiments reveal that this learned representation is highly sensitive to the underlying physics of the quantum simulator, even in non-equilibrium conditions.

The VAE successfully uncovers signatures of frozen-in solitons following rapid cooling, demonstrating its ability to detect topological defects. Furthermore, the model reveals anomalous post-quench dynamics, identifying behaviors not captured by conventional correlation-based methods. The researchers measured the relative phase field of the Bose gases, treating it as a discrete quantity, and used this data to train the VAE. By tuning the tunnel coupling, the strength of the cosine interaction within the model can be controlled. The team’s VAE successfully identified a minimal parametric representation of the stochastic process governing phase fluctuations without prior knowledge of the Hamiltonian or noise sources. This breakthrough delivers a powerful new tool for analyzing quantum simulations and extracting hidden information from complex experimental data, paving the way for scalable, data-driven discovery in quantum many-body systems.

Machine Learning Extracts Sine-Gordon Coupling Parameters

This research demonstrates a successful application of machine learning to the analysis of data from analog quantum simulators, specifically tunnel-coupled one-dimensional Bose gases which model the sine-Gordon field theory. By employing a variational autoencoder, scientists developed a method to extract a minimal set of parameters characterizing the system directly from interference measurements, achieving this without prior knowledge of the underlying physical model. The autoencoder autonomously identified the key coupling parameter by balancing reconstruction accuracy with latent space regularization, and accurately reproduced the statistical properties of the simulated processes. Applying this trained model to non-equilibrium scenarios revealed new insights into system dynamics.

Following a rapid cooling protocol, the latent representation clearly identified frozen-in soliton defects at the level of individual trajectories. Furthermore, in response to a sudden change in tunnel coupling, the autoencoder detected deviations from expected equilibrium behaviour, suggesting the post-quench dynamics may extend beyond the limitations of the current theoretical framework. These findings highlight the potential of variational autoencoders to analyse limited and noisy data from quantum simulators, offering a complementary approach to traditional methods and paving the way for data-driven discoveries in this field.

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🗞 Learning Minimal Representations of Many-Body Physics from Snapshots of a Quantum Simulator
🧠 ArXiv: https://arxiv.org/abs/2509.13821