Quantum many-body systems

Latest papers

• When are bosonic Gaussian states classical to learn?

  Senrui Chen, Antonio Anna Mele, Francesco Anna Mele, John Preskill · 23 September 2026

  A fundamental question in physics is: When does classical behavior emerge from quantum systems? Bosonic Gaussian states provide a natural setting to explore this quantum-classical boundary, as they capture both the classical field behavior and the intrinsic quantum nature of light. Here, we address …

• Hyperbolic Restricted Boltzmann Machine Neural Quantum State

  H. L. Dao · 23 September 2026

  We construct the first type of non-Euclidean non-autoregressive neural quantum state (NQS) in the form of the hyperbolic Restricted Boltzmann Machine (HRBM), which is studied in the variational Monte-Carlo (VMC) setting of the Quantum Sherrington-Kirkpatrick (QSK) model whose ground state exhibits v…

• Gradient-estimator design overcomes trainability barriers in neural-network-based variational optimization

  Yi-Ran Xue, Rui Wang, Baigeng Wang, Chenan Wei · 22 September 2026

  Neural networks provide expressive representations for scientific computing. However, even sufficiently expressive networks can suffer training failure in weak-gradient regimes, limiting their practical use in quantum many-body physics and ab initio quantum chemistry. Here we derive an unbiased dire…

• Physics-Informed Classical and Quantum Neural Networks for One-Dimensional Schrodinger Eigenvalue Problems

  Tariq Mahmood, Waqas Arshad, Bilal Naseer, Alfredo Raya · 22 September 2026

  The Schrodinger equation in one spatial dimension admits a small set of exactly solvable potentials that serve as natural proving grounds for any new eigenvalue solver. We formulate Physics-Informed Neural Networks (PINNs) and Physics-Informed Quantum Neural Networks (PIQNNs) for the time-independen…

• Do Quantum Models Scale Like LLMs?

  David S. Berman, Ying-Jer Kao, Roger G. Melko, Alexander G. Stapleton · 21 September 2026

  In this work, we study the neural scaling laws of RydbergGPT, an autoregressive transformer model trained on qubit projective measurement data gathered from interacting Rydberg atom arrays. The quantum system is known to exhibit a finite-size remnant of a critical point as the laser detuning paramet…

• TetrisCNN for interpretable detection of phases of matter from experimental quantum simulator data

  Kacper Cybi\'nski, Bj\"orn van Zwol, James Enouen, Guillaume Bornet, Thierry Lahaye, Antoine Browaeys, Antoine Georges, Anna Dawid · 18 September 2026

  Detecting phases of matter in general relies on identifying the correct order parameter - a task that remains notoriously difficult for unknown transitions and traditionally is guided by physical intuition and educated guess. Neural networks have recently offered an alternative route by locating pha…

• An ab initio foundation model of wavefunctions that accurately describes chemical bond breaking

  Adam Foster, Zeno Sch\"atzle, P. Bern\'at Szab\'o, Lixue Cheng, Jonas K\"ohler, Gino Cassella, Nicholas Gao, Jiawei Li, Frank No\'e, Jan Hermann · 14 September 2026

  Reliable description of bond breaking remains a major challenge for quantum chemistry due to the multireference character of the electronic structure in dissociating species. Multireference methods in particular suffer from large computational cost, which under the normal paradigm has to be paid ane…

• Learning structural balance of graphs from quantum spectral features

  Stefano Scali, Oleksandr Kyriienko · 11 September 2026

  We develop a quantum approach to spectral feature extraction from the density of states (DOS) of a problem-dependent Hamiltonian, and apply it to machine learning on signed graphs. We propose to embed a signed graph as an Ising model instance with positive and negative interactions, and use the stan…

• Topology Obstructs Pure Foundation Neural Quantum States

  Timothy Heightman, Elena Orlova, Philip Mantrov, Aleksei Ustimenko · 9 September 2026

  Foundation models for ground states in spin-1/2 systems are a promising method for problems ranging from quantum chemistry to identifying new phase diagrams. Nearly all such models are currently pure-states that condition on the Hamiltonian's parameters, whose Monte Carlo samples give energy estimat…

• Data Driven Equation Discovery for Phase-Ordering Dynamics : From Allen Cahn to the Ising Model

  Partha Sarathi Mondal, Manav Kumar Jalan, Anish Kumar, Shradha Mishra · 4 September 2026

  Data-driven discovery of governing equations from spatiotemporal data offers a promising route to obtaining coarse-grained descriptions of complex dynamical systems. Here, we investigate the performance of PDE-SINDy for discovering phase-ordering dynamics using the Allen--Cahn equation as a benchmar…

• Sharp Mixed Spectral Barron Regularity of Coulombic Many-Electron Wave Functions

  Pingbing Ming, Hao Yu · 2 September 2026

  We establish sharp mixed spectral Barron regularity for eigenfunctions of molecular Coulomb Hamiltonians. The mixed norm is a Fourier $L^1$ norm with one isotropic weight and coordinate-product weights, and therefore detects regularity invisible to the isotropic Barron scale. For a nonempty set $I$ …

• A Human-AI Theorem Connecting Spontaneous and Field-Induced Mechanisms of Collective Behavior in One Dimension

  Weiguo Yin · 2 September 2026

  Can an artificial intelligence (AI) generate a scientific hypothesis outside a human collaborator's active hypothesis space (AHS), and can human-AI research be organized to make such breakthroughs more likely? We document such a case while proving a theorem that connects two basic organizing mechani…

• Compositional Dynamics in Learning and Mechanics

  David I. Spivak · 25 August 2026

  We give a single compositional setting in which gradient-based learning and Hamiltonian-style mechanics appear as functorial semantics. The syntax is an operad Arr whose objects are input-output interfaces (pairs of manifolds) and whose morphisms are *smooth adaptive arrangements*, which consist of …

• Scalable quantum simulation of continuous-time generative models via tensor networks

  Nathan X. Kodama, L. Andrew Wray, Sam Cochran, Chad Rigetti, Shravan Veerapaneni, Michael J. Keiser · 25 August 2026

  Continuous-time flow and diffusion models are widely used across many application domains, from large-scale deployment in computer vision and protein folding to emerging adoption for modeling language, time series, and quantum states. After training, inferring statistical properties from continuous-…

• Deep neural networks as lattice gauge theories

  Ro Jefferson, Shradha Ramakrishnan · 21 August 2026

  We modify the NN/QFT duality [1] to incorporate the layerwise permutation symmetry of the network, resulting in a $(0\!+\!1)$-dimensional lattice gauge theory, in which each layer of $N$ neurons acts as an $N$-component lattice site, and the weight matrices play the role of gauge fields living on th…

• Quantum Tensor Network Learning with DMRG

  Gustav J L Jäger, Martin B Plenio, Hans-Martin Rieser · 20 August 2026

  Tensor Networks are a relatively new machine learning approach. The architectures proposed initially are inspired by approaches from quantum many-body physics simulations. One common layout is the matrix product state (MPS) also known as a tensor train optimized with gradient descent techniques. We …

• Infrared Universality of Collective Dynamics across Transformer and State-Space Architectures

  Byung Gyu Chae · 20 August 2026

  Whether distinct neural architectures develop common collective dynamics remains an open question. Recent analysis of Transformer language models revealed a nearly flat, weakly infrared-enhanced time-scale density of states (TDOS) associated with near-marginal long-memory dynamics. Here we test whet…

• Fiber Fingerprints of Hidden Learning-State Dynamics

  Qinyou Wang · 18 August 2026

  A learning system can occupy execution states that are indistinguishable under every declared present-behavior readout yet respond differently to future training. We formalize this through fiber fingerprints: controlled future-learning response laws restricted to present-behavior equivalence classes…

• Spinning Conformal Correlators from Neural Networks

  Manas Dogra, James Halverson, Joydeep Naskar · 18 August 2026

  We construct spinning conformal fields from neural networks and the embedding formalism, computing their two-, three- and four-point functions in examples, building on scalar conformal field techniques introduced in \cite{Halverson:2024axc}. For a particular ensemble of i.i.d. neurons we recover the…

• Hamilton-Zero: A Neural Tensor-Network Foundation Model for Ground States of Arbitrary Quadratic Qubit Hamiltonians

  Timothy Heightman, Elena Orlova, Philip Mantrov, Aleksei Ustimenko · 13 August 2026

  A central promise of useful quantum advantage is the ability to compute ground states of Hamiltonian systems beyond the reach of classical simulation methods. Here we demonstrate that this problem can be effectively amortized across an arbitrary and universal set of Hamiltonians by a foundation mode…

• Clustered Attractor Manifolds and Dynamical Condensation in Self-Attention

  Qucheng Gao, Zuyi Yang, Xiao Chen · 11 August 2026

  Transformer layers generate state-dependent interaction networks: token representations determine the attention matrix, which in turn updates the representations. We study this feedback in a minimal normalized self-attention dynamics and identify the overlap gap as the central quantity governing its…

• Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks

  Bj\"orn Ladewig, Ibrahim Talha Ersoy, Karoline Wiesner · 10 August 2026

  A scientific theory of deep learning, comprising learning dynamics and statistical properties of learned models, is rapidly gaining attention. One of the corner stones of this development are analytically solvable toy models, allowing for the fully tractable analysis of the learning dynamics. Here w…

• Statistical Mechanics of Learning on Product Wasserstein Manifolds

  Srinivasa Rao P Vangmayi P Reddy · 4 August 2026

  Normally the statistical mechanics of learning treats constraints on weight distributions as restrictions that shrink the space of possible solutions. Therefore, it reduces model capacity. In this paper we would like to take a contrary approach, which, however, is based on the earlier work on distri…

• Temperature-driven inversion and nonlinear dynamics in ChatGPT-like AIs

  Neil F. Johnson, Frank Yingjie Huo, Bella Xinrui Li · 4 August 2026

  Increasing the temperature of an ordinary many-state system increases access to a wider range of states and hence increases its entropy. We find the opposite in ChatGPT-like AIs, even though raising the decoder temperature likewise increases access to a wider range of states (next-token choices). Ac…

• Grokking on the Weight-Decay Clock: A Rate Hierarchy from Softly Broken Symmetries

  Taeyoung Kim · 28 July 2026

  Delayed generalization, or grokking, remains poorly understood despite extensive empirical study. We identify an exactly solvable late-time relaxation mechanism for grokking in linear models trained with full-batch heavy-ball optimization and weight decay, together with a locally quadratic extension…