Quantum Many-Body Physics

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4 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

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Latest papers 34

Oct 7, 2026hep-th

Fast holographic inversion of superconducting domes

A holographic superconductor whose scalar mass depends on the gauge field strength,

M(\Fsq)

, reproduces a superconducting dome for a suitable

M

, and recovering that

M

from a given dome has so far taken days for a single training run. We propose a new way of training this model, with which an inversion takes from about ten minutes to an hour. Training needs the gradient of the condition that fixes the critical temperature, which the earlier method obtains by finite differences, repeating the bulk integrations for every training parameter. Here that condition is obtained, without any fit, from two integrations started at the horizon and at the boundary, and its derivative with respect to

M

is an integral over the same two solutions, so the gradient needs no integration of its own. We use the speed to study the part of

M

that a dome cannot determine, on the interval between the value

\Fsq

takes at the horizon for the lowest doping and

\Fsq=0

, at which

M

is the scalar mass

M(0)

that fixes the dimension of the dual operator. We hold the scalar mass at several values, which we call pinned masses, retrain everything else at each, and find that the reconstructions agree wherever the horizons of the dome reach, including the minima of

M

, and differ only on that interval. A rule that keeps the reconstruction with the simplest closed form recovers both the scalar mass and the mass function of a test dome. On Gaussian and double-Gaussian domes and on the measured phase diagrams of YBa

_{2}

Cu

_{3}

O

_{y}

and 2M-WS

_{2}

, however, the pinned mass it keeps rests on ties or on narrow margins, so for these targets the scalar mass is left open. The dome thus constrains

M

where its horizons reach, and fixing the dimension of the dual operator needs a second observable.

Sejin Kim

Center for AI and Natural Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea

Inverse Problems Quantum Many-Body Physics

Oct 5, 2026quant-ph

Out-of-control Hamiltonian Learning

Learning the Hamiltonian of a many-body system from its dynamics is a central task in quantum science, yet the algorithms with the strongest provable guarantees assume some level of quantum control--fast, arbitrary single-qubit gates interleaved with time evolution, and measurements in arbitrary bases--that is beyond the capabilities of near-term analog quantum simulators. Motivated by analog atom- and ion-based platforms, we study Hamiltonian learning under minimal access models. Uniform state preparation and measurements: We first consider the setting where in every experiment, one can rotate each qubit to the same state, perform short-time evolution, and measure every qubit in the same basis. Surprisingly, we show that for generic 2-local Hamiltonians on any interaction graph, all of the parameters can be reconstructed from such experiments. Computational basis state preparation and measurements: We then consider a similarly constrained setting, but where state preparation and measurement are restricted to the computational basis. For nearest-neighbor Hamiltonians with only Pauli

X/Z

interactions, a class which captures contemporary Rydberg atom platforms, we show that over 1D and 2D rectangular lattices, all of the parameters can be reconstructed from such experiments up to unavoidable gauges. Our protocols introduce new techniques for solving structured polynomial systems over an extensive number of parameters. Taken together, our results suggest that one can learn a great deal from the dynamics of quantum many-body systems even under the most stringent experimental constraints.

Weiyuan Gong, Muzhou Ma, Sitan Chen +2

Harvard University. · Caltech. · Oratomic.

Quantum Many-Body Physics Hamiltonian Dynamics

Sep 27, 2026quant-ph

Terminal-Register Certification for Finite-Measurement Learning of Multiscale Quantum States

Structured quantum-state learning not only depends on an expressive ansatz but also on an operational certificate that stays meaningful with finite measurements and imperfect implementation. We study pure one dimensional states learning by an inverse binary multiscale entanglement renormalization ansatz (MERA). In the learning procedure, the qubits removed during coarse graining are controlled coherently and measured together at the terminal register. We confirm that an ideal sequential and terminal measurement schedule delivers the same complete bit string distribution under matched causal operations, while normalized postselection can amplify perturbations inversely with prefix acceptance. A noise aware theorem introduces an individual calibrated total variation implementation budget to the finite shot certificate. The protocol is estimated on an open boundary transverse field Ising ground state. A frozen 8-qubit schedule using

560

million simulated training measurements per run achieves fidelity above

0.99

in all

60

held-out runs, with a mean fidelity of

0.996886

. 1080 circuit-noise cells and 6480 confidence-coverage rows are covered by fixed-circuit robustness validation without a locked soundness violation. We then address architectural fairness at

n=16

using three new studies. In a 120-run exact-gradient multistart diagnostic, MERA has higher fidelity in 58/60 paired restarts and lower long-range error in 60/60, although no run met the prespecified stationarity criterion. Finally, a causal cone-complete, parameter matched local circuit achieves

2.62\times

greater aggregate gate exposure yet loses all 30 paired comparisons in fidelity, long-range error, energy, and entropy.

Bhvain Makwana, Kashyap Patel, Manjunath Joshi +1

Dhirubhai Ambani University, Gandhinagar, Gujarat, India · Georgia Institute of Technology, Atlanta, Georgia, USA

Quantum State Tomography Quantum Machine Learning Quantum Many-Body Physics

Sep 22, 2026quant-ph

Hyperbolic Restricted Boltzmann Machine Neural Quantum State

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 volume-law entanglement. Across a 512-fold increase in the Hilbert space dimension corresponding to a system size increase from

N=14

to

N=24

, HRBM NQS robustly outperforms its Euclidean version, the RBM NQS, in terms of better ground state energy optimization as well as lower Renyi-2

S_2

and von Neumann

S_{vN}

absolute entanglement entropy reconstruction errors. More importantly, for all tested QSK system sizes, HRBM NQS demonstrates a superior expressivity in faithfully reproducing the entire entanglement spectrum of the QSK model from the top eigenvalues down to the tail end across 15 orders of magnitude, while RBM NQS consistently overestimates the sub-dominant modes. This work furnishes a proof-of-concept demonstrating that hyperbolic non-autoregressive NQS ansatze, thanks to the exponential volume of the hyperbolic geometry underlying their constructions, might be more natural at representing volume-law quantum systems than conventional Euclidean NQS. Furthermore, an interesting byproduct of this work is the polynomial scaling result of RBM-type NQS ansatze in the QSK volume-law system as the Hilbert space dimension increases exponentially.

H. L. Dao

Neural Quantum States Quantum Many-Body Physics Restricted Boltzmann Machines Hyperbolic Representation Learning

Sep 17, 2026quant-ph

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

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 phase transitions in known models without any a priori physical knowledge. Yet these approaches remain black boxes and only identify phases without elucidating their properties. Moreover, they often struggle when confronted with realistic, noisy experimental data, which constitute the ultimate testbed for automated methods in physics. Here, we bridge these perspectives by introducing TetrisCNN, a convolutional architecture with parallel branches of differently shaped filters, reminiscent of Tetris blocks, that learns sparse, interpretable latent representations directly in terms of spin correlators. Applied to experimental snapshots of two-dimensional Ising and XY quantum simulators measured in multiple bases, the network not only detects phase transitions and crossovers but also expresses its latent representation and decision boundaries as symbolic formulas built from experimentally measurable spin correlators. This framework opens the way to integrating interpretable neural networks with quantum simulators to uncover and understand new phases of matter.

Kacper Cybiński, Björn van Zwol, James Enouen +5

Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland · IDEAS Research Institute, Królewska 27, 00-060 Warsaw, Poland · Applied Quantum Algorithms ⟨aQaL⟩, LIACS & LION, Leiden University, The Netherlands +7

Quantum Machine Learning Neural Network Interpretability Convolutional Neural Networks Quantum Many-Body Physics

Sep 7, 2026quant-ph

Topology Obstructs Pure Foundation Neural Quantum States

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 estimates according to the variational principle. In this contribution, we show that this representation is topologically obstructed. For any gapped Hamiltonian family whose ground-state bundle is non-trivial, every continuous normalized state-vector model has zero fidelity with the ground state at some parameter value in the Hamiltonian family. For that value, the energy is at least one spectral gap,

Δ

, with an

O(Δ)

gap in an open-neighbourhood of that point. We show that this is a sufficient no-go also in the case of degenerate ground-state manifolds, time dynamics, and periodic systems with mixed space-time topology, demonstrating these obstructions on one- and two-qubit systems. We discuss how this causes a spike in the fidelity susceptibility, giving a numerical signature of a phase-transition where there is none. We then show that operator-valued models canonically avoid these obstructions and preserve topological information, implying a structural necessity in representation for foundation neural quantum states.

Timothy Heightman, Elena Orlova, Philip Mantrov +1

1ICFO–Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain · 2Simulacra Research Inc., London, UK and Chicago, USA

Neural Quantum States Quantum Many-Body Physics

Sep 1, 2026math.AP

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

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

of electron indices on which the wave function is antisymmetric, we derive an explicit admissible region for the isotropic order

s

and the coordinate orders

α,β

. This region is optimal as a uniform statement over the class of clamped-nuclei Coulomb Hamiltonians. For fixed-spin components with two occupied spin blocks, it reduces to

s+α+β<1

; in the fully spin-polarized class it reduces to

s+α<1

. In particular, if

\mathcal I_σ

denotes the family of occupied same-spin blocks determined by

σ

, then every fixed-spin spatial component

ψ_σ

satisfies, for every

0\leqα<1

,

\left(\sum_{I\in\mathcal I_σ}\prod_{i\in I}\langleξ_i\rangle^α\right)\widehat{ψ_σ}\in L^1(\mathbb{R}^{3N}).

For a fully spin-polarized state,

\mathcal I_σ=\{\{1,\ldots,N\}\}

.

Pingbing Ming, Hao Yu

Quantum Chemistry Quantum Many-Body Physics

Aug 12, 2026quant-ph

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

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 model with

\sim0.5

B variational parameters, trained with contemporary techniques from large language models and deep reinforcement learning. To do this, we formulate

\text{spin-}1/2

quantum ground-state learning as manifold variational optimisation over centrally odd scalar functions on

\mathrm{SU}(2)^N

. This replaces explicit Hilbert-space vector amplitudes with manifold functions on which the Hamiltonian acts through Lie derivatives, evaluated by custom automatic differentiation primitives. We prove that the resulting variational principle on this manifold preserves the

\text{spin-}1/2

sector's ground-state upper bound using the Peter-Weyl theorem, then pre-train our foundation model on a dataset of hundreds of thousands of different Hamiltonian systems, varying the connection topology, system size, interaction types and strengths, bringing together a century of many-body literature. Using a novel

\mathrm{SU}(2)

replica-exchange Langevin sampler and sharded natural-gradient optimisation, we train our model with our own extension of the Kronecker-Factored Approximate Curvature (KFAC) optimiser on system sizes up to 64 qubits. On a held-out generalisation dataset, we fine-tune our model on system sizes of up to 1024 qubits, and evaluate on systems up to 8100 qubits.

Timothy Heightman, Elena Orlova, Philip Mantrov +1

1ICFO – Institut de Ci`encies Fot`oniques, The Barcelona Institute of Science and Technology · Castelldefels, Barcelona, Spain · 2Simulacra Research Inc., London, UK & Chicago, USA

Tensor Networks Neural Quantum States Quantum Many-Body Physics

Jul 21, 2026quant-ph

Enhanced Neural Quantum State via Annealed Gradient Descent

Neural quantum states offer expressive representations of quantum many-body wave functions, yet their practical accuracy can be limited by stochastic optimization rather than representational capacity. Here we identify a finite-sample instability, termed subspace trapping, in which physically important configurations become strongly underestimated, remain absent from successive sampling batches and receive insufficient gradient feedback. This self-reinforcing loss of sampled support can confine optimization to an effective subspace and produce apparently stationary states above the true ground state energy. To address this problem, we introduce annealed gradient descent (AGD), a sampling-aware update with annealing factor that temporarily increases the relative contribution of sampled low-probability configurations while limiting the dominance of high-probability ones. We establish the connection between finite-sample support loss and effective subspace optimization, and then evaluate the method across molecular systems, one and two-dimensional

J_1

-

J_2

models. Annealed gradient descent suppresses metastable trapping, preserves physically relevant configurations and enables compact neural quantum states to attain chemical accuracy and competitive state-of-the-art performance. These results establish AGD as a lightweight complement to expressive neural architectures, improved sampling strategies for scalable quantum many-body optimization.

Shiwei Zhou, Yiming Huang, Xiao Yuan +1

Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China · China Center of Advanced Science and Technology, Beijing 100190, China · Center on Frontiers of Computing Studies, School of Computer Science, Peking University, Beijing 100871, China

Neural Quantum States Gradient Descent Quantum Many-Body Physics

Jul 12, 2026quant-ph

Learning Topological Quantum Phases from Limited Subsystems

Characterizing quantum topological phases requires measuring non-local string order parameters, demanding access to the full system, which is often experimentally unfeasible. In this work, we introduce a data-efficient supervised learning framework that circumvents this limitation by recognizing quantum phases from small subsystems. Our protocol utilizes a quantum kernel constructed from the reduced density matrices of these subsystems, which can be efficiently estimated experimentally. We benchmark our framework with the classification of the phase diagrams of two spin models on one-dimensional lattices, namely the generalized cluster-Ising spin-1/2 chain and the anisotropic Haldane spin-1 chain. Remarkably, our approach achieves high accuracy in phase classification when operations are limited to as few as one to four sites, and it also generalizes to longer chains even when trained on moderate system sizes. These findings demonstrate that local reduced density matrices preserve vital signatures of global topological phases, offering a practical route to characterize rich phase diagrams of quantum many-body systems.

Mehran Khosrojerdi, Sougato Bose, Alessandro Cuccoli +3

Department of Physics and Astronomy, University of Florence, via G. Sansone 1, I-50019 Sesto Fiorentino (FI), Italy · Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom · INFN Sezione di Firenze, via G. Sansone 1, I-50019, Sesto Fiorentino (FI), Italy +2

Quantum Many-Body Physics

Jul 7, 2026quant-ph

Provable learning separation for predicting time-evolution of quantum many-body systems

Given that quantum computers are naturally suited to simulate the behavior of quantum many-body systems, an immediate question arises: can one formulate physically motivated quantum machine learning (QML) tasks that exhibit learning separations? We address this problem by studying the learnability of quantum many-body dynamics from the perspective of probably approximately correct (PAC)-learning. Concretely, we devise a supervised learning problem where the training set consists of specifications of randomized stabilizer probe states, evolution times sampled uniformly from a polynomially large time interval

[0,T]

, coupled with expectation values of certain observables evaluated on the resulting time-evolved state under an unknown Hamiltonian. For this learning task, we provide an efficient quantum procedure whose training phase learns the underlying Hamiltonian from short-time training samples, and whose deployment phase combines Hamiltonian simulation with the classical shadows protocol to perform inference on a newly given data point. By contrast, the existence of

O(\mathsf{poly}(n))

-time instances ensures classical hardness: by embedding a

\mathsf{BQP}

-complete computation into the polynomially long time-dynamics of a low-intersection variant of the Feynman-Kitaev clock Hamiltonian construction, we show that, for a certain family of input distributions, no randomized classical polynomial-time algorithm can fulfill our learning condition, unless

\mathsf{BQP}\subseteq\mathsf{P/poly}

. Furthermore, we show that the classically hard instance maintains quantum learnability. We also give an interpretation of our results in learning-assisted certified quantum simulation. Taken together, our results demonstrate a rigorous learning separation for a natural ML task based on Hamiltonian evolution, while building connections between quantum learning theory, quantum simulation, and QML.

Rahul Bandyopadhyay, Riccardo Molteni, Jens Eisert +2

⟨aQaL⟩, Applied Quantum Algorithms, Leiden University, The Netherlands · Leiden Institute of Advanced Computer Science (LIACS), Leiden University, Einsteinweg 55, 2333 CC, Leiden, The Netherlands · Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany +2

Quantum Machine Learning Quantum Many-Body Physics

Jul 2, 2026cs.LG

One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective

Neural quantum states (NQS) provide a flexible and scalable framework for approximating quantum many-body wavefunctions. Among NQS parameterizations, autoregressive models are especially attractive because they enable exact, independent sampling from the Born distribution, avoiding the autocorrelation and mixing issues of Markov chain methods. Yet their optimization remains comparatively underexplored: Adam is a scalable method but ignores function space geometry, while stochastic reconfiguration is principled but costly and numerically fragile in large models. To address this gap, we show that variational energy minimization can be viewed as an advantage policy-gradient problem over the Born distribution, motivating trust-region optimization for NQS training. We introduce Proximal Wavefunction Optimization (PWO), a principled trust-region algorithm that clips probability-ratio changes in the amplitude channel and phase increments in the phase channel. PWO avoids explicit matrix inversion, reuses samples across multiple updates, and combines the scalability of first-order optimization with theoretical guarantees. Across Ising and frustrated

J_1

-

J_2

one- and two-dimensional spin systems, PWO improves stability and wall-clock convergence over Adam, minSR, and SPRING. Finally, we fine-tune a

1.5

B-parameter RWKV-7 model, demonstrating NQS optimization at a scale over three orders of magnitude beyond prior work.

Juan Agustín Duque, Sergio García Heredia, Vinicius Hernandes +4

Mila Quebec AI Institute, Université de Montréal, Montréal, Canada · Applied Quantum Algorithms ⟨aQaL⟩, LIACS & LION, Leiden University, Leiden, Netherlands · QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, Netherlands +1

Neural Quantum States Second-Order Optimization Policy Gradient Methods Trust-Region Optimization Quantum Many-Body Physics

Jul 1, 2026quant-ph

Mechanistic Interpretability and Causal Feature Steering of Neural Quantum States via Sparse Autoencoders

Neural Quantum States (NQS) are a remarkably expressive class of variational ansätze for quantum many-body wavefunctions, yet little is understood about their internal mechanisms: trained on variational objectives alone, how do NQS accurately capture physical observables that they have never been explicitly optimized for? In this work, we present a systematic approach to analyze the internal activations of NQS using sparse autoencoders. We extract features from the residual stream and demonstrate that these features strongly correlate with physical observables such as order parameters, staggered magnetization, and half-chain correlators, across both ground state representation and real-time dynamics. Remarkably, the discovery of these features is entirely unsupervised, with no physical labels provided. We further establish that such features causally affect the corresponding observables predicted by NQS, by showing that targeted, post-training intervention on a \textit{single} feature smoothly and monotonically steers the corresponding observable, while leaving the variational energy nearly unchanged. These results demonstrate that NQS are not merely functional approximators, but encode rich, interpretable internal representations of physical information. Our approach provides both a diagnostic and an intervention tool for NQS, and serves as a foundation for using mechanistic interpretability towards more reliable, transparent NQS.

Zihao Qi, Christopher Earls

Department of Physics, Cornell University, Ithaca, NY 14853, USA. · Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA.

Neural Quantum States Mechanistic Interpretability Quantum Many-Body Physics

Jul 1, 2026cond-mat.str-el

Holographic Quantum Transformer: A Generalist Neuro-Symbolic Architecture for Solving Frustrated Systems via Generative Attention

Simulating two-dimensional frustrated quantum matter is a grand challenge due to the sign problem and exponential Hilbert space complexity. In this work, we introduce the Holographic Quantum Transformer (HQT), a physics-inspired generative architecture that leverages global self-attention to resolve non-local entanglement patterns. We validate HQT on the square lattice

J_1-J_2

Heisenberg model. On the heavily frustrated

8 \times 8

lattice at the quantum critical point (

J_2=0.5

), HQT reaches a ground-state energy per site (

E/N

) of

\mathbf{-0.5001(1)}

, consistent with the expected finite-size scaling trend. Beyond numerical accuracy, HQT exhibits intrinsic physical awareness, autonomously recovering the underlying

J_2

interaction geometry through interpretable attention maps. Our central contribution is ``Holographic Transfer", a zero-shot size-extrapolation protocol with rapid alignment: a model trained on

8 \times 8

systems is directly projected onto larger

10 \times 10

lattices via continuous positional-embedding interpolation and head re-initialization, achieving high-fidelity initialization and rapid convergence. This zero-shot protocol yields an energy of

E/N = \mathbf{-0.49782(3)}

, statistically consistent with the variational state of the art while requiring no from-scratch training on the target lattice. Our results establish generative attention as a scalable paradigm for transferable quantum simulation.

Xingran Guo, Tiaojie Xiao, Jie Liu +1

National University of Defense Technology Changsha, China · State University of New York at New Paltz New Paltz, NY, USA

Neural Quantum States Zero-Shot Learning Transformer Attention Quantum Many-Body Physics

Jun 29, 2026quant-ph

Learning the structure of open quantum systems

We design an algorithm for learning the coefficients of an

n

-qubit constant-local Lindbladian to

\varepsilon

error with

O(g d^2 \log(n) / \varepsilon^2)

total evolution time, where

g

is the single-site energy and

d

is the (approximate) degree of the interaction graph. Though Lindbladians present new challenges not present in the special case of Hamiltonians, our algorithm achieves the suite of desiderata attained by state-of-the-art Hamiltonian learning algorithms: (1) it uses non-adaptive, ancilla-free randomized Pauli measurement circuits with a time resolution of only

Θ(1/g)

; (2) it works without knowledge of the structure of the unknown Lindbladian; (3) it depends on a smooth form of degree, thereby supporting the learning of quasi-local and power-law Lindbladians. Our algorithm is a simple iterative method, where the objective function consists of Fourier coefficients of the Lindbladian restricted to few-site regions. Its analysis identifies the difficulty unique to open systems, which we call "confusing" terms. For settings where the "confusion" is limited, the performance of the algorithm improves. We demonstrate this for the case of structure learning of Hamiltonians from access to real-time evolution, where we obtain a new algorithm that is significantly simpler than previous work. In addition, using the same iterative method, we design the first efficient algorithm for structure learning Hamiltonians from high-temperature Gibbs states.

Laura Lewis, Ewin Tang, John Wright

UC Berkeley

Quantum System Identification Quantum Machine Learning System Identification Quantum Many-Body Physics

Jun 24, 2026cs.LG

Is Variational Monte Carlo Robust? Sharp Moment Thresholds and Heavy-tailed Stochastic Optimization

Variational Monte Carlo (VMC) is a central algorithm in electronic structure theory and has gained renewed importance through modern neural-network ansätze such as FermiNet. At its core, VMC seeks ground states by minimizing the Rayleigh quotient by stochastic optimization. In this work, we show that the resulting stochastic optimization problem is intrinsically governed by the nodal geometry of the underlying wave function. More precisely, we establish that properties of the nodal set determine the integrability of the local energy and gradient estimators that drive VMC. For broad and practically relevant ansatz classes, including Slater-Jastrow wave functions with variable-exponent Slater-type orbitals, we prove that these estimators are generically heavy-tailed and fail to admit higher moments. At the same time, for general analytic ansätze, we prove weak moment bounds for the relevant estimators and identify precise low-moment regimes, showing how generic and degenerate nodal structures lead to different integrability thresholds. Building on this analysis, we introduce a new robust variant of VMC

\unicode{x2013}

coined PS-Clip-VMC

\unicode{x2013}

which is based on clipping both the local energy and the gradient random variable. We prove that PS-Clip-VMC converges both in expectation and with high probability in the weak moment regime of VMC. Preliminary experiments for training FermiNet on Atoms with up to 18 electrons suggest that PS-Clip-VMC is significantly more robust than standard methods.

Philipp Grohs, Davide Nobile

Faculty of Mathematics, University of Vienna · RICAM, Austrian Academy of Sciences

Stochastic Optimization Quantum Chemistry Quantum Many-Body Physics Heavy-Tailed Stochastic Optimization

Jun 24, 2026quant-ph

Two-dimensional Hyperbolic RNN Neural Quantum State

In the first part of this work, we construct the first type of two-dimensional (2D) hyperbolic neural quantum state (NQS) in the form of the Lorentz 2DRNN (Recurrent Neural Network) and benchmark its performance against the Euclidean 2DRNN in the paradigmatic

N\times N

2D Transverse Field Ising Model (2DTFIM) setting with different lattice sizes up to

N=12

and at different transverse magnetic field strengths. We find that hyperbolic Lorentz 2DRNN NQS definitively outperform Euclidean 2DRNN NQS when the system is at the phase transition point when the physics can be described by a conformal field theory (CFT), which is known to be dual to an Anti-de-Sitter (AdS) space whose spatial geometry is hyperbolic. In the second part of this work, we benchmark the performances of the recently introduced one-dimensional (1D) hyperbolic NQS including Poincaré RNN/GRU and Lorentz RNN/GRU against their Euclidean NQS versions in

N\times N

2DTFIM, which has to be converted to a one-dimensional setting to allow for the use of 1D NQS. The findings in this case extend our previous results that 1D hyperbolic NQS definitively outperform 1D Euclidean NQS, thanks to the combined effects of the hierarchical structure comprising the first and

N^{th}

neighbor interactions present in the 1D system arising from the 2D lattice and the CFT physics at the critical point. While more studies with larger system sizes are required, our work serves as a proof-of-concept for the utility, effectiveness as well as the superior performances of one- and two-dimensional hyperbolic NQS ansatzes compared to the existing Euclidean NQS in many-body quantum physics systems, especially when these systems exhibit structural hierarchy or when they are at criticality, or a combination of both.

H. L. Dao

Neural Quantum States Recurrent Neural Networks Quantum Many-Body Physics Hyperbolic Representation Learning

Jun 14, 2026quant-ph

Learning ground state observables from quantum computing experiments

Recent theoretical progress has established conditions under which machine learning models can efficiently predict ground-state properties of gapped local Hamiltonians when trained on quantum-generated data. Previous experimental demonstrations in this paradigm, however, have largely been limited to small systems or highly structured states, due to the difficulty of preparing many-body ground states on quantum processors. In this work, we demonstrate learning from experimental quantum data generated from approximate ground states of the two-dimensional Heisenberg XXZ model with system sizes up to 115 qubits. We construct a dataset of single-site expectation values, two-point correlations, and 12-body loop correlations across the antiferromagnetic phase. We then train neural networks on this data and show that they can accurately predict spatially resolved observables for previously unseen Hamiltonian parameters, both within the training distribution and in an out-of-distribution regime approaching the phase boundary. Our results demonstrate the practical realization of learning from quantum data for an interacting two-dimensional many-body system at scale, motivating a path toward regimes where quantum processors could provide training data beyond the reach of classical approximation methods.

Ben Jaderberg, Freya Shah, Minjun Jeon +3

IBM Quantum, IBM Research Europe, Hursley, Winchester, SO21 2JN, United Kingdom · Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom · IBM Quantum, T. J. Watson Research Center, Yorktown Heights, NY 10598, USA +4

Quantum Machine Learning Quantum Many-Body Physics

Jun 11, 2026cond-mat.dis-nn

Low-variance estimators overcome the phase-gradient bottleneck in complex-valued neural quantum states

Complex neural quantum states are difficult to optimize when their wavefunction phase carries gauge, chiral, fermionic, or topological structure. We show that the major failure mode is not only ansatz expressivity, but the Monte Carlo estimator used to learn this phase. For separated amplitude-phase states, differentiating the local energy at fixed samples gives a different unbiased estimator of the same variational Monte Carlo phase force, without changing the objective. We further extend the construction to coupled two-head networks by keeping the amplitude-gradient contribution and applying the direct derivative only to the phase path. An adaptive minimum-variance mixture interpolates between standard and direct estimators during training. Across flux ladders, chiral chains, two-dimensional flux cylinders, an interacting fermion ladder, shared-network controls, and a fractional quantum Hall benchmark, the resulting estimators reduce phase-gradient variance, suppress seed failures, and often move multi-percent standard-gradient plateaus to sub-percent accuracy.

Yi-Ran Xue, Rui Wang, Baigeng Wang +1

*National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China. · Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA. · Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China. +3

Neural Quantum States Complex-Valued Neural Networks Quantum Many-Body Physics Variance Reduction

Jun 5, 2026cond-mat.mtrl-sci

Agentic multi-fidelity learning of quasiparticle and excitonic properties

Many-body GW-Bethe-Salpeter equation calculations are essential for accurate simulations of electronic structure and optical properties in modern low-dimensional nanomaterials. However, these methods are computationally demanding and can exhibit localized numerical instabilities or convergence failures that are difficult to detect within high-throughput workflows. We introduce an agent-guided multi-fidelity framework for correcting GW-Bethe-Salpeter excited-state landscapes in strained MoS2-WS2 bilayers. Across stacking registries, strain branches and reciprocal-space samplings, the workflow identifies spike-like excursions, near-zero-gap collapse and cross-fidelity inconsistencies associated with fragile long-wavelength dielectric screening. A structural agent evaluates calculations by assigning confidence weights and selectively using a small number of high-accuracy reference points. Machine learning models then transfer information across related systems and apply Gaussian process corrections to recover improved quasiparticle gaps and exciton binding energies, with calibrated uncertainty estimates. The approach corrects numerically induced artifacts without erasing physical strain dependence and substantially improves agreement with higher-fidelity references relative to a no-agent baseline. These results show that reliable surrogate learning for excited-state materials requires explicit diagnosis of numerical fragility, not direct interpolation of raw first-principles data points. The proposed framework is readily transferable to other optoelectronic nanomaterials characterized by strong quantum confinement, such as quantum dots, nanoribbons, layered two-dimensional semiconductors, and hybrid perovskite nanostructures.

Arnab Neogi, Aaron Forde, Christopher A. Lane +2

Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA · Center for Integrated Nanotechnologies, Materials Physics and Applications Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

AI Agents for Scientific Discovery Materials Property Prediction Quantum Many-Body Physics Computational Materials Science

May 29, 2026physics.comp-ph

Physically Constrained Ensemble Gaussian Process Modelling for Expensive Quantum Systems with Heteroskedastic Noise

Accurate modeling of quantum many-body systems often requires computationally expensive simulations such as Density Matrix Renormalization Group (DMRG) or Quantum Monte Carlo (QMC) calculations. These methods, while precise, impose significant time and resource constraints, limiting their use in exhaustive parameter exploration. Moreover, these expensive simulations can contain variable errors over the large unknown parameter space, which needs to be quantified and propagated. Thus, predictive modelling is required to estimate the functional space accurately over scarcely sampled data with heteroskedastic noise, while preserving the physical relevance of the estimation. Therefore, we present a Physically Constrained Ensemble Gaussian Process (pc-EGP) framework designed to efficiently model complex and noisy quantum systems under physical consistency constraints. The proposed method first enforces physical constraints as a user controlled weighted penalty to the data-driven loss function of the Gaussian Process (GP) surrogates. Then an ensemble of such GP models is trained with variable noisy simulations via numerical quadrature method where these multiple GP(s) at different nodes is integrated as a quadrature weighted average. We first demonstrate the framework on synthetically generated data before applying to quantum systems. In the first case study, we leverage DMRG simulations of the Bose-Hubbard Model to predict the critical interaction parameter Uc governing the superfluid-to-Mott-insulator transition. In the second case study, we demonstrate our method on QMC simulations, of a quantum liquid confined inside a nanoporous silicate with the goal of optimizing a chemical environment to realize a one-dimensional superfluid. Compared to conventional GP, pc-EGP achieves a better balance of accuracy and physically meaningful predictions.

Arpan Biswas, Sutirtha Paul, Joseph Agada +2

University of Tennessee-Oak Ridge Innovation Institute, University of Tennessee, Knoxville, TN 37996, USA · Institute for Advanced Materials and Manufacturing, University of Tennessee, Knoxville, Tennessee 37996, USA · Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA. +2

Surrogate Modeling Uncertainty Quantification Heteroscedastic Regression Physics-Informed ML Quantum Many-Body Physics Gaussian Process Regression

May 28, 2026quant-ph

Attention-based optimizer for symmetry finding

Finding symmetries is crucial for understanding physical models. In this work, we present an optimization framework that searches Pauli symmetries of Hamiltonians, merging the fields of machine learning with automated symmetry finding. Built on a Set-Transformer architecture, our framework uses self-attention to encode the pairwise and higher-order correlations among the Pauli-Strings. The relations are then decoded as a candidate, which is further optimized with a custom commutation-based objective, and mapped to a symmetry of the input Hamiltonian. We apply our method to random Pauli Hamiltonians, periodic one and two dimensional transverse-field Ising model and the Toric code. We show that for physical Hamiltonians (Ising and Toric), our framework succeeds with near-deterministic probability while providing substantial advantage compared to state-of-the-art strategies. For random Pauli Hamiltonians, we estimate the required computational resources, specifically the number of parallel starts and the number of GPUs, to find a symmetry with high success probability under fixed design specifications.

Shreya Banerjee, Vinodh Raj Rajagopal Muthu, Charlie Nation +5

Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom · Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada · QuAOS collaboration

Quantum Many-Body Physics Neural Combinatorial Optimization

May 26, 2026cond-mat.str-el

Neural Autoregressive Control Variates for the Quantum Monte Carlo Sign Problem

We train a pair of autoregressive models to construct zero-mean control variates to mitigate the sign problem in quantum Monte Carlo simulations. The two autoregressive networks are confined to the positive- and negative-sign sectors with strictly disjoint support, and each is exactly normalized over its sector. Their difference is therefore structurally zero-mean, providing an unbiased auxiliary observable whose correlation with the sign estimator controls the variance reduction. We implement the method within the stochastic series expansion framework, which we extend to frustrated lattices by developing an incremental loop-topology update. Sign-ergodic sampling is achieved through a twist channel, which is the unique sign-changing mechanism on non-bipartite lattices. We implement the control variates as autoregressive transformers with an end-of-sequence parity mask that enforces exact sign-sector resolution, while the incremental loop-count change and cumulative frustration parity are incorporated as topological features. On the triangular-lattice Heisenberg antiferromagnet, we benchmark the method in the small-

N

limit. The control variate reduces the standard error of the average sign by up to an order of magnitude and that of the energy estimator by a factor of three to five, remaining effective even when the average sign drops below

10^{-3}

. This work lays out the framework and provides a proof-of-principle demonstration that autoregressive control variates can effectively mitigate the sign problem. Scaling to larger systems with physics-informed architectures is the subject of future work.

Bei Qiao, Lei Wang

Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China · University of Chinese Academy of Sciences, Beijing 100049, China

Quantum Many-Body Physics Variance Reduction Autoregressive Modeling

May 21, 2026cond-mat.str-el

Comment on "Spin-1/2 Kagome Heisenberg Antiferromagnet: Machine Learning Discovery of the Spinon Pair-Density-Wave Ground State"

A recent article [Phys. Rev. X 15, 011047 (2025)] utilizes group-equivariant convolutional neural networks to study the ground state of the kagome Heisenberg antiferromagnet. On the largest finite-size cluster studied to date (

N=108

), the authors report variational energies significantly lower than other numerical methods, including state-of-the-art density matrix renormalization group (DMRG) calculations. In contrast to previous results suggesting a possible spin-liquid ground state, the authors observe a spinon pair-density-wave ground state. We find that: (i) the reported low energies are artifacts of broken ergodicity in the Metropolis--Hastings sampling, since the single-spin-flip update rule utilized by the authors effectively freezes the Markov chains; and (ii) when ergodic sampling is enforced via spin-exchange updates, the neural network converges to energies significantly higher than existing DMRG results, calling the paper's claims into question.

Helia Kamal, Dominik Kufel, DinhDuy Vu +2

Department of Physics, Harvard University, Cambridge, MA 02138, USA · Harvard Quantum Initiative, Cambridge, MA 02138, USA · Department of Physics, Boston University, Boston, MA 02215, USA

Neural Quantum States Markov Chain Monte Carlo Quantum Many-Body Physics

May 19, 2026cond-mat.str-el

Representability-Aware Neural Networks for Reduced Density Matrices: Application to Fractional Chern Insulators

We develop a representability-aware and interpolable neural network (NN) framework for predicting two-particle reduced density matrices (2-RDMs). The NN incorporates a subset of representability conditions through its architecture and loss function, and can operate on different momentum meshes, enabling evaluating the representability conditions across multiple meshes, which we call interpolated representability condition. The framework can be used either to predict 2-RDMs on large momentum meshes by interpolating exact results from small meshes, or as a variational 2-RDM ansatz optimized by energy minimization on arbitrary meshes. We apply this approach to the fractional Chern insulator in the one-band projected model of twisted bilayer MoTe

_2

at twist angle

3.89^\circ

and hole filling

2/3

. Trained on exact-diagonalization (ED) 2-RDMs from meshes with

12

or

18

momentum points using six different NN architectures, the best NN is the residual multilayer perceptron, which predicts the

6\times6

2-RDM with

97.07\%-98.18\%

accuracy relative to the ED 2-RDM but predicts an energy

77.353

meV above ED ground-state energy. We then variationally optimize the NN on several meshes including

6\times6

, predicting a

6\times 6

energy of just

0.104

meV below ED while maintaining

98.94\%-98.96\%

accuracy. Compared with the conventional boundary-point semidefinite programming, which gives an energy

5.560

meV below ED with

96.40\%-98.94\%

accuracy, the NN achieves a more accurate energy and similar accuracy while using only less than 1/20 as many parameters. Eventually, we add a symmetric mesh of

48

momentum points to the variational optimization of the NN, and provide a prediction of the many-body ground-state energy and the many-body quantum metric on that mesh.

Justin B. Hart, Awwab A. Azam, Thomas Li +4

Department of Physics, University of Florida, Gainesville, FL, USA · Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL, USA · Palo Alto High School, Palo Alto, CA, USA +4

Quantum Machine Learning Quantum Many-Body Physics Computational Materials Science

May 18, 2026cond-mat.quant-gas

Can machine learning for quantum-gas experiments be explainable?

Virtually all aspects of many-body atomic physics are challenging: experiments are technically demanding, datasets have become enormous, and the memory and CPU requirements for classical simulation of generic quantum systems often scale exponentially with system size. Machine learning (ML) methods are already assisting in each of these areas and are poised to become transformative. Here, we focus on two specific applications of ML to cold-atom-based quantum simulators. These devices generally generate data in the form of images; we first showcase denoising of raw images and then identify solitonic waves in Bose-Einstein condensates. In both of these examples, we comment on the interplay between performance, model complexity, and interpretability.

I. B. Spielman amd J. P. Zwolak

National Institute of Standards and Technology, Gaithersburg, MD 20899, USA · Department of Physics, University of Maryland, College Park, MD 20742, USA · Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA

Interpretable ML Scientific ML Quantum Many-Body Physics Image Denoising

May 13, 2026cond-mat.str-el

Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo

Neural-network quantum states have emerged as a powerful variational framework for quantum many-body systems, with recent progress often driven by massively parallel architectures such as transformers. Recurrent neural network quantum states, however, are frequently regarded as intrinsically sequential and therefore less scalable. Here we revisit this view by showing that modern recurrent architectures can support fast, accurate, and computationally accessible neural quantum state simulations. Using autoregressive recurrent wave functions together with recent advances in parallelizable recurrence, we develop variational ansätze, called parallel scan recurrent neural quantum states (PSR-NQS), which can be trained efficiently within variational Monte Carlo in one and two spatial dimensions. We demonstrate accurate benchmark results and show that, with iterative retraining, our approach reaches two-dimensional spin lattices as large as

52\times52

while remaining in agreement with available quantum Monte Carlo data. Our results establish recurrent architectures as a practical and promising route toward scalable neural quantum state simulations with modest computational resources.

Ejaaz Merali, Mohamed Hibat-Allah, Mohammad Kohandel +2

Department of Physics and Astronomy, University of California, Davis, California 95616, USA · Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada · Vector Institute, Toronto, Ontario, M5G 0C6, Canada +1

Neural Quantum States Recurrent Neural Networks Quantum Many-Body Physics

Apr 28, 2026cond-mat.str-el

QERNEL: a Scalable Large Electron Model

We introduce QERNEL, a foundational neural wavefunction that variationally solves families of parameterized many-electron Hamiltonians and captures their ground states throughout parameter space within a single model. QERNEL combines FiLM-based parameter conditioning with scale-efficient architectural elements -- mixture of experts and grouped-query attention, substantially improving expressivity at low computational cost. We apply QERNEL to interacting electrons in semiconductor moiré heterobilayers, training a single weight-shared model for systems of up to 150 electrons. By solving the many-electron Schrödinger equation conditioned on moiré potential depth, QERNEL captures both quantum liquid and crystal states and discovers the sharp phase transition between them, marked by abrupt changes in interaction energy and charge density. Our work establishes a foundation model for moiré quantum materials and a scalable architecture toward a Large Electron Model for solids.

Khachatur Nazaryan, Liang Fu

Department of Physics, Massachusetts Institute of Technology, Cambridge, MA-02139,USA

Neural Quantum States Materials Science Quantum Many-Body Physics Quantum Neural Networks

Apr 28, 2026cond-mat.mtrl-sci

Kohn-Sham Hamiltonian from Effective Field Theory: Quasiparticle Band Narrowing from Frozen Core Dynamics

Kohn-Sham (KS) eigenvalues are routinely compared with angle-resolved photoemission (ARPES) and used as input for many-body methods, yet density functional theory (DFT) assigns them no physical meaning. For alkali and alkaline-earth metals, KS bandwidths overestimate ARPES measurements by 20-35%, a discrepancy that persists across all exchange-correlation functionals. We construct an effective field theory (EFT) of the inhomogeneous electron gas and show that two conditions imply KS bands are the quasiparticle bands, up to a frozen-core renormalization factor zcore: a scale separation between core excitation energies and the valence Fermi energy, and an approximate Galilean invariance of the uniform electron gas confirmed by diagrammatic Monte Carlo. This factor reflects dynamical core excitations that conventional pseudopotentials freeze out and no static potential can capture. The correction 1-zcore reaches 20-35% for alkali metals but falls below 5% for Al and Si, explaining both the failure and success of KS band theory. We derive a closed-form post-SCF formula and validate it for Li, Na, K, Ca, Mg, Al, and Si; the predicted quasiparticle bands resolve the long-standing ARPES bandwidth discrepancy, matching embedded dynamical mean-field theory at negligible cost. This work also exemplifies first-principles agentic science, a direction particularly suited to the AGI-for-Science paradigm: an LLM-co-developed derivation with controlled approximations, verified symbolically and against a few experiments, becomes a deterministic harness for agentic scale-out, resolving simultaneously the LLM audit bottleneck and the non-falsifiability of fit-based AI-for-science.

Xiansheng Cai, Han Wang, Kun Chen

Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China

Quantum Many-Body Physics Computational Materials Science

Apr 27, 2026cond-mat.quant-gas

Uncovering Exotic Paired States in the 2D Spin-Imbalanced Fermi Gas with Neural Wave Functions

We study the zero-temperature phase diagram of the 2D spin-imbalanced Fermi gas with short-ranged attractive interactions using the recently developed neural network variational Monte Carlo method with the AGPs FermiNet Ansatz. The Fulde-Ferrell-Larkin-Ovchinnikov phase is observed in the weakly interacting BCS limit and a polarised superfluid is seen in the strongly interacting BEC limit. When the interactions are strong, the minority-spin momentum density is reduced almost to zero in the momentum-space region occupied by the unpaired majority-spin electrons. When the interactions are very strong, phase separation occurs, with regions containing bosonic pairs and unpaired regions occupied by the remaining majority-spin particles. In addition, we observe translational symmetry breaking at intermediate interaction strengths, where the system forms an exotic crystal of Cooper pairs in a Fermi fluid of unpaired majority-spin particles. We provide a possible explanation for the formation of the crystalline phase, explain the origins of the k-space momentum-density hole when the pairs are tightly bound, and discuss how our approach opens new directions for future work.

Wan Tong Lou, Gino Cassella, Andres Perez Fadon +5

Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom · 2DeepMind, 6 Pancras Square, London N1C 4AG, United Kingdom · Department of Physics TQM, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany +1

Phase Transitions Quantum Many-Body Physics