arXiv subjects

Markus Heyl

Publications and source records attributed to Markus Heyl.

At least 37 records · Page 2Linked to original sources

arXiv2025

Empowering deep neural quantum states through efficient optimization

Computing the ground state of interacting quantum matter is a long-standing challenge, especially for complex two-dimensional systems. Recent developments have highlighted the potential of neural quantum states to solve the quantum many-body problem by encoding the many-body wavefunction into artificial neural networks. However, this method has faced the critical limitation that existing optimization algorithms are not suitable for training modern large-scale deep network architectures. Here, we introduce a minimum-step stochastic-reconfiguration optimization algorithm, which allows us to train deep neural quantum states with up to $10^6$ parameters. We demonstrate our method for paradigmatic frustrated spin-1/2 models on square and triangular lattices, for which our trained deep networks approach machine precision and yield improved variational energies compared to existing results. Equipped with our optimization algorithm, we find numerical evidence for gapless quantum-spin-liquid phases in the considered models, an open question to date. We present a method that captures the emergent complexity in quantum many-body problems through the expressive power of large-scale artificial neural networks.

cond-mat.dis-nn↗

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↗

arXiv2025

Subsystem Evolution Speed as Indicator of Relaxation

In studying the time evolution of isolated many-body quantum systems, a key focus is determining whether the system undergoes relaxation and reaches a steady state at a given point in time. Traditional approaches often rely on specific local operators or a detailed understanding of the stationary state. In this letter, we introduce an alternative method that assesses relaxation directly from the time-dependent state by focusing on the evolution speed of the subsystem. The proposed indicator evaluates the rate of change in the reduced density matrix of the subsystem over time. We demonstrate that in systems reaching relaxation, as the overall system size increases, the evolution speed of sufficiently small yet still finite-sized subsystems notably diminishes. This leads to small fluctuations in the expectation values of operators, which is also consistent with the predictions made by the eigenstate thermalization hypothesis. We apply this approach across various models, including the chaotic Ising chain, XXZ chains with and without many-body localization, and the transverse field Ising chain. Our results confirm the robustness and accuracy of subsystem evolution speed as a reliable indicator for relaxation.

quant-ph↗

arXiv2025

Characterizing dynamical criticality of many-body localization transitions from the Fock-space perspective

Characterizing the nature of many-body localization transitions (MBLTs) and their potential critical behaviors has remained a challenging problem. In this work, we study the dynamics of the displacement, quantifying the spread of the radial probability distribution in the Fock space, for three systems with MBLTs, i.e., the Hamiltonian models with quasiperiodic and random fields, as well as a random-circuit Floquet model of a MBLT. We then perform a finite-size scaling analysis of the long-time averaged displacement by considering two types of ansatz for MBLTs, i.e., continuous and BKT transitions. The data collapse based on the assumption of a continuous phase transition with power-law correlation length reveals that the scaling exponent of the MBLT induced by random field is close to that of the Floquet model, but significantly differes from the quasiperiodic model. Additionally, we find that the BKT-type scaling provides a more accurate description of the MBLTs in the random model and the Floquet model, yielding larger (finite-size) critical points compared to those obtained from power-law scaling. Our work highlights that the displacement is a valuable tool for studying MBLTs, as relevant to ongoing experimental efforts.

quant-ph↗

arXiv2025

Probing prethermal nonergodicity through measurement outcomes of monitored quantum dynamics

Projective measurements are a key element in quantum physics and enable rich phenomena in monitored quantum dynamics. Here, we show that the measurement outcomes, recorded during monitored dynamics, can provide crucial information about the properties of the monitored dynamical system itself. We demonstrate this for a Floquet model of many-body localization, where we find that the prethermal many-body localized regime becomes unstable against rare measurements, yielding an unusual enhancement of quantum entanglement. Through an unsupervised learning and mutual information analysis on the classical dataset of measurement outcomes, we find that the information loss in the system, reflected by the increased entanglement, is compensated by an emergent structure in this classical dataset. Our findings highlight the crucial role of measurements and corresponding classical outcomes in capturing prethermal nonergodicity, offering a promising perspective for applications to other monitored quantum dynamics.

quant-ph↗

arXiv2025

Convolutional transformer wave functions

Deep neural quantum states have recently achieved remarkable performance in solving challenging quantum many-body problems. While transformer networks appear particularly promising due to their success in computer science, we show that previously reported transformer wave functions haven't so far been capable to utilize their full power. Here, we introduce the convolutional transformer wave function (CTWF). We show that our CTWFs exhibit superior performance in ground-state search and non-equilibrium dynamics compared to previous results, demonstrating promising capacity in complex quantum problems.

cond-mat.dis-nn↗

arXiv2025

Probing quantum many-body dynamics using subsystem Loschmidt echos

The Loschmidt echo - the probability of a quantum many-body system to return to its initial state following a dynamical evolution - generally contains key information about a quantum system, relevant across various scientific fields including quantum chaos, quantum many-body physics, or high-energy physics. However, it is typically exponentially small in system size, posing an outstanding challenge for experiments. Here, we experimentally investigate the subsystem Loschmidt echo, a quasi-local observable that captures key features of the Loschmidt echo while being readily accessible experimentally. Utilizing quantum gas microscopy, we study its short- and long-time dynamics. In the short-time regime, we observe a dynamical quantum phase transition arising from genuine higher-order correlations. In the long-time regime, the subsystem Loschmidt echo allows us to quantitatively determine the effective dimension and structure of the accessible Hilbert space in the thermodynamic limit. Performing these measurements in the ergodic regime and in the presence of emergent kinetic constraints, we provide direct experimental evidence for ergodicity breaking due to fragmentation of the Hilbert space. Our results establish the subsystem Loschmidt echo as a novel and powerful tool that allows paradigmatic studies of both non-equilibrium dynamics and equilibrium thermodynamics of quantum many-body systems, applicable to a broad range of quantum simulation and computing platforms.

cond-mat.quant-gas↗

arXiv2024

Adaptive Trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws

Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer timesteps, and increased error rate on account of the larger circuit depth. We present an adaptive Trotterization algorithm to cope with time-dependent Hamiltonians, where we propose a concept of piecewise "conserved" quantities to estimate errors in the time evolution between two (nearby) points in time; these allow us to bound the errors accumulated over the full simulation period. They reduce to standard conservation laws in the case of time-independent Hamiltonians, for which we first developed an adaptive Trotterization scheme [PRX Quantum 4, 030319]. We validate the algorithm for a time-dependent quantum spin chain, demonstrating that it can outperform the conventional Trotter algorithm with a fixed step size at a controlled error.

quant-ph↗

arXiv2024

Simplicity of mean-field theories in neural quantum states

The utilization of artificial neural networks for representing quantum many-body wave functions has garnered significant attention, with enormous recent progress for both ground states and non-equilibrium dynamics. However, quantifying state complexity within this neural quantum states framework remains elusive. In this study, we address this key open question from the complementary point of view: Which states are simple to represent with neural quantum states? Concretely, we show on a general level that ground states of mean-field theories with permutation symmetry only require a limited number of independent neural network parameters. We analytically establish that, in the thermodynamic limit, convergence to the ground state of the fully-connected transverse-field Ising model (TFIM), the mean-field Ising model, can be achieved with just one single parameter. Expanding our analysis, we explore the behavior of the 1-parameter ansatz under breaking of the permutation symmetry. For that purpose, we consider the TFIM with tunable long-range interactions, characterized by an interaction exponent $α$. We show analytically that the 1-parameter ansatz for the neural quantum state still accurately captures the ground state for a whole range of values for $0\le α\le 1$, implying a mean-field description of the model in this regime.

quant-ph↗

arXiv2024

Learning effective Hamiltonians for adaptive time-evolution quantum algorithms

Digital quantum simulation of many-body dynamics relies on Trotterization to decompose the target time evolution into elementary quantum gates operating at a fixed equidistant time discretization. Recent advances have outlined protocols enabling more efficient adaptive Trotter protocols, which have been shown to exhibit a controlled error in the dynamics of local observables and correlation functions. However, it has remained open to which extent the errors on the actual generator of the dynamics, i.e., the target many-body Hamiltonian, remain controlled. Here, we propose to use quantum Hamiltonian learning to numerically obtain the effective Hamiltonian and apply it on the recently introduced ADA-Trotter algorithm as a concrete demonstration. Our key observation is that deviations from the target generator remain bounded on all simulation times. This result suggests that the ADA-Trotter not only generates reliable digital quantum simulation of local dynamics, but also controllably approximates the global quantum state of the target system. Our proposal is sufficiently general and readily applicable to other adaptive time-evolution algorithms.

quant-ph↗

arXiv2024

Vortex loop dynamics and dynamical quantum phase transitions in 3D fermion matter

Over the past decade, dynamical quantum phase transitions (DQPTs) have emerged as a paradigm shift in understanding nonequilibrium quantum many-body systems. However, the challenge lies in identifying order parameters that effectively characterize the associated dynamic phases. In this study, we investigate the behavior of vortex singularities in the phase of the Green's function for a broad class of fermion lattice models in three dimensions after an instantaneous quench in both interacting and non-interacting systems. We find that the full set of vortices form one-dimensional dynamical objects, which we call \emph{vortex loops}. We propose that the number of such vortex loops can be interpreted as a quantized order parameter that distinguishes between different non-equilibrium phases. Our results establish an explicit link between variations in the order parameter and DQPTs in the non-interacting scenario. Moreover, we show that the vortex loops are robust in the weakly interacting case, even though there is no direct relation between the Loschmidt amplitude and the Green's function. Finally, we observe that vortex loops can form complex dynamical patterns in momentum space. Our findings provide valuable insights for developing definitions of dynamical order parameters in non-equilibrium systems.

cond-mat.stat-mech↗

arXiv2024

Quantum hard disks on a lattice

We formulate a quantum version of the hard-disk problem on lattices, which exhibits a natural realization in systems of Rydberg atoms. We find that quantum hard disks exihibit unique dynamical quantum features. In 1D, the crystal melting process displays ballistic behavior as opposed to classical sub-diffusion. For 2D, crystal structures remain intact against most defects, whereas classically they are washed out completely. We link this peculiar quantum behavior to quantum many-body scars. Our study highlights the potential of constrained 2D quantum matter to display unique dynamical behaviors.

quant-ph↗

arXiv2023

Dynamical localization transition of string breaking in quantum spin chains

The fission of a string connecting two charges is an astounding phenomenon in confining gauge theories. The dynamics of this process have been studied intensively in recent years, with plenty of numerical results yielding a dichotomy: the confining string can decay relatively fast or persist up to extremely long times. Here, we put forward a dynamical localization transition as the mechanism underlying this dichotomy. To this end, we derive an effective string breaking description in the light-meson sector of a confined spin chain and show that the problem can be regarded as a dynamical localization transition in Fock space. Fast and suppressed string breaking dynamics are identified with delocalized and localized behavior, respectively. We then provide a further reduction of the dynamical string breaking problem onto a quantum impurity model, where the string is represented as an "impurity" immersed in a meson bath. It is shown that this model features a localization-delocalization transition, giving a general and simple physical basis to understand the qualitatively distinct string breaking regimes. These findings are directly relevant for a wider class of confining lattice models in any dimension and could be realized on present-day Rydberg quantum simulators.

cond-mat.str-el↗

arXiv2023

Identifying quantum many-body integrability and chaos using eigenstates trace distances

While the concepts of quantum many-body integrability and chaos are of fundamental importance for the understanding of quantum matter, their precise definition has so far remained an open question. In this work, we introduce an alternative indicator for quantum many-body integrability and chaos, which is based on the statistics of eigenstates by means of nearest-neighbor subsystem trace distances. We show that this provides us with a faithful classification through extensive numerical simulations for a large variety of paradigmatic model systems including random matrix theories, free fermions, Bethe-ansatz solvable systems, and models of many-body localization. While existing indicators, such as those obtained from level-spacing statistics, have already been utilized with great success, they also face limitations. This concerns for instance the quantum many-body kicked top, which is exactly solvable but classified as chaotic in certain regimes based on the level-spacing statistics, while our introduced indicator signals the expected quantum many-body integrability. We discuss the universal behaviors we observe for the nearest-neighbor trace distances and point out that our indicator might be useful also in other contexts such as for the many-body localization transition.

cond-mat.stat-mech↗

arXiv2023

Making Trotterization adaptive and energy-self-correcting for NISQ devices and beyond

Simulation of continuous time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision, but it inevitably leads to increased computational efforts. This is particularly costly for today's noisy intermediate scale quantum computers, where notable gate imperfections limit the circuit depth that can be executed at a given accuracy. Classical adaptive solvers are well-developed to save numerical computation times. However, it remains an outstanding challenge to make optimal usage of the available quantum resources by means of adaptive time steps. Here, we introduce a quantum algorithm to solve this problem, providing a controlled solution of the quantum many-body dynamics of local observables. The key conceptual element of our algorithm is a feedback loop which self-corrects the simulation errors by adapting time steps, thereby significantly outperforming conventional Trotter schemes on a fundamental level and reducing the circuit depth. It even allows for a controlled asymptotic long-time error, where usual Trotterized dynamics is facing difficulties. Another key advantage of our quantum algorithm is that any desired conservation law can be included in the self-correcting feedback loop, which has potentially a wide range of applicability. We demonstrate the capabilities by enforcing gauge invariance which is crucial for a faithful and long-sought quantum simulation of lattice gauge theories. Our algorithm can be potentially useful on a more general level whenever time discretization is involved concerning, for instance, also numerical approaches based on time-evolving block decimation methods.

quant-ph↗