arXiv subjects

Markus Schmitt

Publications and source records attributed to Markus Schmitt.

At least 19 recordsLinked to original sources

arXiv2026

Geometric inflation of deviations challenges neural quantum states in dynamics of quantum Ising models

Neural quantum states (NQS) have emerged as a powerful framework for simulating non-equilibrium dynamics in strongly correlated quantum systems, offering scalable variational representations of highly entangled states. Yet, accurate NQS simulations have been found to be surprisingly challenging in some physical regimes of limited complexity. Here, we address paradigmatic quench dynamics of a one-dimensional quantum Ising model as a controlled benchmark. Through supervised state reconstruction we establish substantially tighter empirical upper bounds on the required parameter count than previous estimates, ruling out representational limitations as the key obstruction. Instead, we uncover a geometric inflation of small deviations as a hitherto overlooked challenge for accurate solutions of the infinitesimal time-dependent variational principle (TDVP): the dynamical rotation of the kernel of the quantum geometric tensor (QGT) can suddenly lend physical significance to previously irrelevant parameter deviations. The stability of matrix product state solutions of the same TDVP suggests that the non-linearity of the neural network ansatz is the origin of the sensitivity. These results identify QGT-null-space rotation as a geometric diagnostic of sensitive NQS dynamics and as a concrete target for improving TDVP algorithms

quant-ph↗

arXiv2026

Neural quantum states in condensed matter: advances, best practices, and prospects

Neural quantum states provide flexible variational representations of quantum many-body wave functions by combining neural-network parametrizations with Monte Carlo sampling. In this perspective, we review recent advances in their application to condensed-matter systems, focusing on frustrated quantum magnets, interacting lattice fermions, and non-equilibrium dynamics. We discuss the architectures, symmetry constraints, optimization methods, and sampling strategies underlying state-of-the-art calculations, and summarize practical guidelines for reliable simulations. We also examine the principal remaining challenges, including learning non-trivial sign and phase structures, controlling variational bias, enforcing physical symmetries, scaling optimization to large networks, and achieving stable real-time evolution. Finally, we outline promising directions in which neural quantum states may extend the reach of classical simulations of strongly correlated quantum matter.

cond-mat.str-el↗

arXiv2026

Exploring the Relaxation Landscape of a 2D Quantum Magnet on a 256-Qubit Processor

How quantum matter relaxes far from equilibrium is a central open problem in many-body physics, and one for which analog quantum simulators are well positioned to move from confirming theory to discovering new physics. Here, we use a two-dimensional Rydberg atom array of 256 qubits to map the relaxation landscape of the two-dimensional transverse-field Ising model across its phase diagram. Beyond the expected rapid thermalization, we identify two further regimes. The first is a prethermal regime whose dynamics are governed by an effective XY model. The second, and most unexpected, is a crossover regime characterized by a slowdown in relaxation. This slowdown occurs precisely where state-of-the-art classical tensor-network methods lose control at late times, whereas the quantum simulation remains consistent across system sizes. These results establish Rydberg atom arrays as a platform for scientific discovery in nonequilibrium quantum many-body dynamics.

quant-ph↗

arXiv2026

Disorder-enhanced compressibility of Floquet random quantum circuits

Current quantum hardware is limited by noise and decoherence, which restrict the depth of unitary circuits that can be implemented with high fidelity. We investigate how the compressibility of time-evolution operators depends on the dynamical regime of the underlying many-body system. As a testbed, we study a one-dimensional Floquet random circuit with a tunable competition between interactions and on-site disorder. Using tensor-network simulations, we characterize operator growth through the operator-entanglement entropy of the Floquet unitary as well as of out-of-time-ordered correlators (OTOCs). We find rapid operator scrambling at weak disorder, while strong disorder leads to slow OTOC-front propagation and logarithmic or near-logarithmic operator-entanglement growth over the accessible time window. We then optimize shallow brickwall circuits to approximate the Floquet evolution and show that strong-disorder circuits can be compressed to substantially smaller depths than weak-disorder circuits at fixed logarithmic fidelity density. These results suggest that localized or slowly scrambling dynamics provide a favorable regime for compressed quantum simulation on noisy devices.

quant-ph↗

arXiv2026

Comment on "Beyond-classical computation in quantum simulation"

A recent article [Science 388, 199-204 (2025)] investigates the applicability of numerical methods and a quantum processor unit in simulating a quantum annealing protocol. One of the findings indicates that Neural Quantum States - a versatile variational ansatz for the many-body wave function based on artificial neural networks - fail to reach the same accuracy as the quantum processor. In this comment we revisit these concerns, demonstrating that NQS can provide competitive results in some of the cases when accounting for the Monte-Carlo noise and large autocorrelation times between samples obtained from the final state.

quant-ph↗

arXiv2026

Machine Learning Optimal Quantum Error Correction Thresholds

As quantum computers remain susceptible to noise, QEC is essential for preserving logical information during computations. However, the performance of QEC codes breaks down beyond certain noise thresholds, revealing fundamental limits on their ability to protect quantum information. These limits can be characterized using information-theoretic measures such as the coherent information, which quantifies the maximum rate at which logical information can be reliably transmitted through a noisy quantum channel. In this work, we establish a direct connection between the CI and the binary cross-entropy loss used when training neural network decoders. Specifically, we show that the CI constitutes a sharp lower bound on the achievable loss for decoders that track logical operators across noisy channels. To this end, we develop a transformer-based neural network model based on maximum likelihood decoding. We train this network to estimate the CI and evaluate its performance on the surface code under three noise models: code capacity, phenomenological, and circuit-level noise. Our results demonstrate that the network accurately predicts CI and yields threshold estimates that closely match known theoretical limits. When used as a decoder, the network significantly outperforms the minimum weight perfect matching decoder in terms of logical error rate. We also introduce a novel soft post-selection scheme that independently treats uncertainty in both logical operators and relies on confidence-based filtering of the network's output. We prove that such post-selection strategies, based on the MLD cosets, are optimal, and demonstrate their scalability in terms of both logical error rate and abort probability. These findings establish transformer-based architectures as powerful tools for QEC and provide the first numerical evidence supporting the optimality and scalability of MLD-based post-selection.

quant-ph↗

arXiv2026

Modeling light-matter coupled systems with neural quantum states

Recent advances in cold atom manipulation enable the study of many-body systems where short-range interactions between neighboring atoms coexist with long-range interactions mediated by photons. Such a combination of interactions makes a theoretical approach challenging beyond mean-field methods. In this work, we develop a neural quantum state based approach to study these systems numerically. We introduce a neural-network architecture capable of handling hybrid Hilbert spaces with large local bosonic dimensions in strongly interacting spin-photon systems. We benchmark this approach on a model of a two-dimensional lattice of Rydberg atoms coupled to a photon mode. The superradiant ground states found in the large spin-photon coupling regime allow us to demonstrate the efficiency of the method in the presence of high photon occupation. Furthermore, the ability to capture spin-spin and spin-photon correlations leads us to observe quantitative deviations in the ground state phase boundaries with respect to mean-field theory. The method extends to other systems with a similar hybrid Hilbert space structure, such as spin-phonon systems, and provides a scalable framework for investigating their ground state properties.

cond-mat.quant-gas↗

arXiv2026

Compressed minimum-purity time evolution for late-time quantum dynamics

Unitary time evolution of initially simple quantum many-body states rapidly generates entanglement and complex correlations, which limits direct numerical simulations. The late-time dynamics of physical observables, however, typically exhibits an effective simplicity in the form of hydrodynamics or kinetic theory. This leads to the question whether microscopic equations of motion can remain accurate and tractable up to long time scales by discarding irrelevant information in a controlled manner. Here, we introduce compressed minimum-purity time evolution (CoMPuTE) as an approach to keep track of a consistent set of reduced local density matrices, closing the hierarchical equations of motion using a minimum-purity principle. In benchmark applications we demonstrate (i) accurate description of energy diffusion in the one-dimensional mixed-field Ising model, (ii) the applicability to genuinely out-of-equilibrium Floquet dynamics starting from a pure state, and (iii) the limitations of the local reduced density matrix approximation when describing transport in the XXZ chain at $\Delta=1$ that is governed by increasingly non-local integrals of motion. The CoMPuTE method enhances computational efficiency in comparison to the closely related local-information time evolution algorithm, opening a possible route towards an extension to systems in higher spatial dimensions.

cond-mat.stat-mech↗

arXiv2026

Neural network modeling of many-body super- and sub-radiant dynamics

There is significant interest in exploring novel phenomena in quantum light-matter interfaces, which are driven by the combination of structured dissipation and long-range interactions that are typical in such systems. To this end, it is important to develop new general numerical simulation techniques, which can access large system sizes and are not based on semi-classical approaches. Here, we report the first application of neural quantum states to obtain the dissipative dynamics of light-matter-coupled systems beyond what is accessible with exact and tensor-network calculations. We specifically apply this method to simulate the many-body emission dynamics of approximately 40 atoms, arranged in dense arrays in one and two dimensions. These systems have been chosen because they can support prominent subradiant dynamics at late times and could be realized with cold atomic quantum simulators.

quant-ph↗

arXiv2026

Time-dependent variational Monte Carlo without bias

When combined with highly expressive ansatz functions such as neural quantum states, variational Monte Carlo (VMC) constitutes a versatile numerical approach to tackle the quantum many-body problem in and out of equilibrium. However, its traditional formulation exhibits a subtle estimation bias leading to inaccuracies, which can be particularly detrimental when addressing real time dynamics. In this work, we investigate two avenues to circumvent said estimation bias. First, we propose an unbiased variant of time-dependent VMC using self-normalized importance sampling with respect to a cutoff-based deformation of the Born distribution. We demonstrate the feasibility and accuracy of the approach in pathological and generic cases of quench dynamics. Furthermore, we explore an alternative sampling strategy based on active learning via the tensor cross interpolation (TCI). While we find that our choice of tensor network architecture lacks the required low rank property, the proposed TCI-based algorithm complements the conventional importance sampling paradigm, providing an alternative perspective that may be further explored in future work.

quant-ph↗

arXiv2025

Operator Lanczos Approach enabling Neural Quantum States as Real-Frequency Impurity Solvers

To understand the intricate exchange between electrons of different bands in strongly correlated materials, it is essential to treat multi-orbital models accurately. For this purpose, dynamical mean-field theory (DMFT) provides an established framework, whose scope crucially hinges on the availability of efficient quantum impurity solvers. Here we present a real-frequency impurity solver based on neural quantum states (NQS) combined with an operator-Lanczos construction. NQS are an asymptotically unbiased variational ground-state ansatz that employs neural networks to capture long-range correlations on complicated graph structures. We leverage this ability to solve multi-orbital impurity problems using a systematically improvable Segmented Commutator Operator-Lanczos (SCOL) construction. Our benchmarks on both the single-orbital Anderson model and the multi-orbital Hubbard-Kanamori impurity Hamiltonian reveal excellent ground-state precision and the capacity to accurately resolve zero temperature spectral functions and self-energies. These results open avenues for extending DMFT to more challenging problems.

cond-mat.str-el↗

arXiv2025

Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics

The quantum dynamics of many-qubit systems is an outstanding problem that has recently driven significant advances in both numerical methods and programmable quantum processing units. In this work, we employ a comprehensive toolbox of state-of-the-art numerical approaches to classically simulate the dynamics of the two-dimensional transverse field Ising model. Our methods include three different tensor network techniques -- matrix product states, tree-tensor networks, and two-dimensional tensor-networks under the belief propagation approximation -- as well as time-dependent variational Monte Carlo with Neural Quantum States. We focus on two paradigmatic dynamical protocols: (i) quantum annealing through a critical point and (ii) post-quench dynamics. Our extensive results show the quantitative predictions of various state-of-the-art numerical methods providing a benchmark for future numerical investigations and experimental studies with the aim to push the limitations on classical and QPUs. In particular, our work connects classical simulability to different regimes associated with quantum dynamics in Rydberg arrays - namely, quasi-adiabatic dynamics, the Kibble-Zurek mechanism, and quantum quenches.

quant-ph↗

arXiv2025

Reinforcement learning entangling operations on spin qubits

High-fidelity control of one- and two-qubit gates past the error correction threshold is an essential ingredient for scalable quantum computing. We present a reinforcement learning (RL) approach to find entangling protocols for semiconductor-based singlet-triplet qubits in a double quantum dot. Despite the presence of realistically modelled experimental constraints, such as various noise contributions and finite rise-time effects, we demonstrate that an RL agent can yield performative protocols, while avoiding the model-biases of traditional gradient-based methods. We optimise our RL approach for different regimes and tasks, including training from simulated process tomography reconstruction of unitary gates, and investigate the nuances of RL agent design.

quant-ph↗

arXiv2025

Learning to stabilize nonequilibrium phases of matter with active feedback using partial information

We investigate the role of information in active feedback control of quantum many-body systems using reinforcement learning. Active feedback breaks detailed balance, enabling the engineering of steady states and dynamical phases of matter otherwise inaccessible in equilibrium. We train reinforcement learning agents using partial state information to prevent entanglement spreading in (1+1)-dimensional stabilizer circuits with up to 128 qubits. We find that, above a critical information threshold, learned near-optimal strategies are non-greedy, stochastic, and reduce volume-law entangled steady states to area-law scaling. The agents achieve this by placing a series of bottlenecks that induce pyramidal structures in the long-time spatial entanglement distribution, which effectively split the system and reduce the maximum accessible entanglement. Crucially, learned strategies are inherently out of equilibrium and require real-time active feedback; we find that the learned behavior cannot be replaced by simple human-designed control rules. This work establishes the foundations for classically implemented, information-driven individual control of many interacting quantum degrees of freedom, demonstrating the capabilities of reinforcement learning to stabilize and uncover novel critical properties of many-body nonequilibrium steady states.

quant-ph↗

arXiv2025

Quantum computing and artificial intelligence: status and perspectives

This white paper discusses and explores the various points of intersection between quantum computing and artificial intelligence (AI). It describes how quantum computing could support the development of innovative AI solutions. It also examines use cases of classical AI that can empower research and development in quantum technologies, with a focus on quantum computing and quantum sensing. The purpose of this white paper is to provide a long-term research agenda aimed at addressing foundational questions about how AI and quantum computing interact and benefit one another. It concludes with a set of recommendations and challenges, including how to orchestrate the proposed theoretical work, align quantum AI developments with quantum hardware roadmaps, estimate both classical and quantum resources - especially with the goal of mitigating and optimizing energy consumption - advance this emerging hybrid software engineering discipline, and enhance European industrial competitiveness while considering societal implications.

quant-ph↗

arXiv2025

Simulating dynamics of correlated matter with neural quantum states

While experimental advancements continue to expand the capabilities to control and probe non-equilibrium quantum matter at an unprecedented level, the numerical simulation of the dynamics of correlated quantum systems remains a pivotal challenge - especially in intermediate spatial dimensions. Neural quantum states are emerging as a new computational tool to investigate the time evolution of many-body quantum systems in previously inaccessible regimes. We review the recent progress in the field with a focus on the different time propagation methods, an overview of the reported applications, and a discussion of the major current challenges.

quant-ph↗

arXiv2025

Roughening dynamics of interfaces in the two-dimensional quantum Ising model

The properties of interfaces are key to understand the physics of matter. However, the study of quantum interface dynamics has remained an outstanding challenge. Here, we use large-scale Tree Tensor Network simulations to identify the dynamical signature of an interface roughening transition within the ferromagnetic phase of the 2D quantum Ising model. For initial domain wall profiles we find extended prethermal plateaus for smooth interfaces, whereas above the roughening transition the domain wall decays quickly. Our results can be readily explored experimentally in Rydberg atomic systems.

quant-ph↗

arXiv2025

Time evolution of the quantum Ising model in two dimensions using Tree Tensor Networks

The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the dynamics of the quantum Ising model in two dimensions. Within the perturbative regime of small transverse fields, TTNs faithfully reproduce analytically known, but non-trivial and physically interesting results, for lattices up to $16 \times 16$ sites. Limitations of the method related to the rapid growth of entanglement entropy are explored within more general, paradigmatic quench settings. We provide and discuss comprehensive benchmarks regarding the benefit of \emph{GPU} acceleration and the impact of using local operator sums on the performance.

quant-ph↗