arXiv subjects

Jannes Nys

Publications and source records attributed to Jannes Nys.

At least 19 recordsLinked to original sources

arXiv2026

Majorana string simulation of nonequilibrium dynamics in two-dimensional lattice fermion systems

The study of real-time dynamics of fermions remains one of the last frontiers beyond the reach of classical simulations and is key to our understanding of quantum behavior in chemistry and materials, with implications for quantum technology. Here we introduce a Heisenberg-picture algorithm that propagates observables expressed in a Majorana-string basis using a truncation scheme that preserves Trotter accuracy and aims at maintaining computational efficiency. The framework is exact for quadratic Hamiltonians -- remaining restricted to a fixed low-weight sector determined by the physical observable -- admits variational initial states, and can be extended to interacting regimes via systematically controlled truncations. We benchmark our approach on one- and two-dimensional Fermi-Hubbard quenches, comparing against tensor network methods (MPS and fPEPS) and recent experimental data. The method achieves high accuracy on timescales comparable to state-of-the-art variational techniques and experiments, demonstrating that controlled Majorana-string truncation is a practical tool for simulating two-dimensional fermionic dynamics.

cond-mat.quant-gas↗

arXiv2026

Real-Time Dynamics in Two Dimensions with Tensor Network States via Time-Dependent Variational Monte Carlo

Reliably simulating two-dimensional many-body quantum dynamics with projected entangled pair states (PEPS) has long been a difficult challenge. In this work, we overcome this barrier for low-energy quantum dynamics by developing a stable and efficient time-dependent variational Monte Carlo (tVMC) framework for PEPS. By analytically removing all gauge redundancies of the PEPS manifold and exploiting tensor locality, we obtain a numerically well-conditioned tVMC equation. This enables long-time evolution in previously inaccessible regimes. We explain how the difficulties in the traditional approach, particularly those associated with gauge redundancies, are resolved within tVMC. We demonstrate the power and generality of the method through five representative real-time local quench dynamics in two dimensions: (I) chiral edge propagation in a free-fermion Chern insulator; (II) vison propagation in a pure Z2 gauge theory; (III) vison confinement dynamics in a Z2 lattice gauge theory coupled to Higgs field; (IV) fractionalized charge transport in a fractional Chern insulator; and (V) superfluidity and critical velocity in interacting bosons. All simulations are performed on >= 10 x 10 lattices with evolution times beyond T = 10 using modest computational resources. In addition, we also simulate the paradigmatic dynamics of the Ising model following a global quench at the critical transverse field, and obtain, with modest bond dimension, agreement with previous results. The method significantly extends the reach of classical tensor-network simulations for studying elementary excitations in quantum many-body systems in real-time and provides a valuable computational counterpart to emerging quantum simulators. As a by-product in the development, we also present a new form of minSR, which is more stable and offers a new perspective on tVMC.

cond-mat.str-el↗

arXiv2026

Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States

Deep learning offers a powerful approach to quantum many-body problems via neural network wavefunctions, but their optimization remains a severe bottleneck. Existing optimization methods, including natural gradient descent and stochastic reconfiguration, suffer from spectral gap-dependent convergence that limits their effectiveness on systems fraught with competing orders and nearly degenerate ground states, such as frustrated magnets and strongly correlated electron materials. Here, we introduce Projected Inverse Iteration (PII) by re-framing the ground-state search as an eigenvalue problem. PII achieves rapid, gap-insensitive convergence while preserving the favorable polynomial computational scaling of stochastic reconfiguration. Demonstrated on challenging two-dimensional spin systems, including the highly frustrated $J_1$-$J_2$ model, PII outperforms standard optimization techniques and presents a promising algorithmic strategy for discovering complex quantum states in the presence of small spectral gaps. More broadly, PII can be interpreted as a novel natural gradient method tailored for eigenvalue problems, opening up its application to related challenges within deep learning.

quant-ph↗

arXiv2026

Stabilizer-based quantum simulation of fermion dynamics with local qubit encodings

Simulating the dynamical properties of large-scale many-fermion systems is a longstanding goal of quantum chemistry, material science and condensed matter. Local fermion-to-qubit encodings have opened a new path for practical fermionic simulations on digital quantum hardware where fermionic statistics are not enforced at the hardware level. In this paper, we explore these local encodings from the perspective of the corresponding time-evolution unitaries. Specifically, we propose a new framework for digital implementations of these qubit-encoded fermionic time-evolution unitaries based on \emph{flow sets}, which are one-dimensional subsets of the directed fermionic interaction graph. We find that any local fermionic encoding, when restricted to a given flow set, adopts a simple structure that we can classify systematically. For each categorized flow-set form, we propose a low-depth qubit quantum circuit that implements the time evolution unitary using the stabilizer formalism. As an application of our construction, we introduce novel flow-based decompositions for known two-dimensional encodings, leading to efficient circuit decompositions of time-evolution unitaries. We generally observe a space-time trade-off, where mappings with larger qubit-to-fermion ratios yield shallower time-evolution quantum circuits.

quant-ph↗

arXiv2025

Fermionic neural Gibbs states

We introduce fermionic neural Gibbs states (fNGS), a variational framework for modeling finite-temperature properties of strongly interacting fermions. fNGS starts from a reference mean-field thermofield-double state and uses neural-network transformations together with imaginary-time evolution to systematically build strong correlations. Applied to the doped Fermi-Hubbard model, a minimal lattice model capturing essential features of strong electronic correlations, fNGS accurately reproduces thermal energies over a broad range of temperatures, interaction strengths, even at large dopings, for system sizes beyond the reach of exact methods. These results demonstrate a scalable route to studying finite-temperature properties of strongly correlated fermionic systems beyond one dimension with neural-network representations of quantum states.

quant-ph↗

arXiv2025

Local fermion-to-qudit mappings: a practical recipe for four-level systems

In this paper, we present a new set of local fermion-to-qudit mappings for simulating fermionic lattice systems. We focus on the use of multi-level qudits, specifically ququarts. Traditional mappings, such as the Jordan-Wigner transformation (JWT), while useful, often result in non-local operators that scale unfavorably with system size. To address these challenges, we introduce mappings that efficiently localize fermionic operators on qudits, reducing the non-locality and operator weights associated with JWT. We propose one mapping for spinless fermions and two mappings for spinful fermions, comparing their performance in terms of qudit-weight, circuit depth, and gate complexity. By leveraging the extended local Hilbert space of qudits, we show that these mappings enable more efficient quantum simulations in terms of two-qudit gates, reducing hardware requirements without increasing computational complexity. We validate our approach by simulating prototypical models such as the spinless t-V model and the Fermi-Hubbard model in two dimensions, using Trotterized time evolution. Our results highlight the potential of qudit-based quantum simulations in achieving scalability and efficiency for fermionic systems on near-term quantum devices.

quant-ph↗

arXiv2025

Accurate ground states of $SU(2)$ lattice gauge theory in 2+1D and 3+1D

We present a neural network wavefunction framework for solving non-Abelian lattice gauge theories in a continuous group representation. Using a combination of $SU(2)$ equivariant neural networks alongside an $SU(2)$ invariant, physics-inspired ansatz, we learn a parameterization of the ground state wavefunction of $SU(2)$ lattice gauge theory in 2+1 and 3+1 dimensions. Our method, performed in the Hamiltonian formulation, has a straightforward generalization to $SU(N)$. We benchmark our approach against a solely invariant ansatz by computing the ground state energy, demonstrating the need for bespoke gauge equivariant transformations. We evaluate the Creutz ratio and average Wilson loop, and obtain results in strong agreement with perturbative expansions. Our method opens up an avenue for studying lattice gauge theories beyond one dimension, with efficient scaling to larger systems, and in a way that avoids both the sign problem and any discretization of the gauge group.

hep-lat↗

arXiv2025

Biorthogonal Neural Network Approach to Two-Dimensional Non-Hermitian Systems

Non-Hermitian quantum many-body systems exhibit a rich array of physical phenomena, including non-Hermitian skin effects and exceptional points, that remain largely inaccessible to existing numerical techniques. In this work, we investigate the application of variational Monte Carlo and neural network wavefunction representations to examine their ground-state (the eigenstate with the smallest real part energy) properties. Due to the breakdown of the Rayleigh-Ritz variational principle in non-Hermitian settings, we develop a self-consistent symmetric optimization framework based on variance minimization with a dynamically updated energy estimate. Our approach respects the biorthogonal structure of left and right eigenstates, and is further strengthened by exploiting system symmetries and pseudo-Hermiticity. Tested on a two-dimensional non-Hermitian transverse field Ising model endowed with a complex longitudinal field, our method achieves high accuracy across both parity-time symmetric and broken phases. Moreover, we propose novel optimization routines that address the challenges posed by exceptional points and provide reliable convergence to the ground state in regimes where standard variational techniques fail. Lastly, we show, through extensive numerical evidence, that our method offers a scalable and flexible computational tool to investigate non-Hermitian quantum many-body systems, beyond the reach of conventional numerical techniques such as the density-matrix renormalization group algorithm.

quant-ph↗

arXiv2025

Functional Neural Wavefunction Optimization

We propose a framework for the design and analysis of optimization algorithms in variational quantum Monte Carlo, drawing on geometric insights into the corresponding function space. The framework translates infinite-dimensional optimization dynamics into tractable parameter-space algorithms through a Galerkin projection onto the tangent space of the variational ansatz. This perspective unifies existing methods such as stochastic reconfiguration and Rayleigh-Gauss-Newton, provides connections to classic function-space algorithms, and motivates the derivation of novel algorithms with geometrically principled hyperparameter choices. We validate our framework with numerical experiments demonstrating its practical relevance through the accurate estimation of ground-state energies for several prototypical models in condensed matter physics modeled with neural network wavefunctions.

cond-mat.str-el↗

arXiv2025

Partial suppression of magnetism in the square lattice SU(3) Hubbard model

The SU(N) Hubbard model is a natural extension of the SU(2) model. However, even the N=3 case remains poorly understood. We report a substantially new ground-state phase diagram of the square lattice SU(3) Fermi-Hubbard model. Using a backflow ansatz, we identify strong signatures of a Mott transition and a subsequent magnetic transition, and the suppression of a previously predicted magnetic phase. We study the hole-doped model, identifying a transition from magnetic to paramagnetic behavior in the strong-coupling regime. Our findings offer a qualitatively new ground state picture. More broadly, our work suggests a path to study general SU(N) Hubbard models with arbitrary filling and geometry.

cond-mat.str-el↗

arXiv2025

Precise Quantum Chemistry calculations with few Slater Determinants

Slater determinants have underpinned quantum chemistry for nearly a century, yet their full potential has remained challenging to exploit. In this work, we show that a variational wavefunction composed of a few hundred optimized non-orthogonal determinants can achieve energy accuracies comparable to the state of the art. This is obtained by introducing an optimization method that leverages the quadratic dependence of the variational energy on the orbitals of each determinant, enabling an exact iterative optimization, and uses an efficient tensor-contraction algorithm to evaluate the effective Hamiltonian with a computational cost that scales as the fourth power of the number of basis functions. We benchmark the accuracy of the proposed method with exact full-configuration interaction results where available, and we achieve lower variational energies than coupled cluster (CCSD(T)) for several molecules in the double-zeta basis.

physics.chem-ph↗

arXiv2025

Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations

Neural networks have shown to be a powerful tool to represent the ground state of quantum many-body systems, including fermionic systems. However, efficiently integrating lattice symmetries into neural representations remains a significant challenge. In this work, we introduce a framework for embedding lattice symmetries in fermionic wavefunctions and demonstrate its ability to target both ground states and low-lying excitations. Using group-equivariant neural backflow transformations, we study the t-V model on a square lattice away from half-filling. Our symmetry-aware backflow significantly improves ground-state energies and yields accurate low-energy excitations for lattices up to 10 x 10. We also compute accurate two-point density-correlation functions and the structure factor to identify phase transitions and critical points. These findings introduce a symmetry-aware framework important for studying quantum materials and phase transitions.

cond-mat.str-el↗

arXiv2024

Phase diagram and crystal melting of helium-4 in two dimensions

We study the zero-temperature phase diagram of two-dimensional helium-4 using neural quantum states. Our variational description allows us to address liquid and solid phases using the same functional form as well as exploring possible melting scenarios, for instance via an intermediate hexatic phase. Notably, this is achieved by performing fixed pressure variational Monte Carlo calculations. Within the isobaric ensemble framework, we are able to clearly identify the first-order liquid-solid phase transition. However, in an intermediate region of nearly constant pressure, we find that simulations of $N=30$ atoms continuously transition from liquid to solid, with signatures of a hexatic order coexisting with a small condensate fraction. Calculations for larger systems follow the metastable liquid and solid branches in this transient region. We additionally compute the Rényi-2 entanglement entropy across the liquid-solid phase transition and find a sharp decrease upon freezing.

cond-mat.stat-mech↗

arXiv2024

Ab-initio variational wave functions for the time-dependent many-electron Schrödinger equation

Understanding the real-time evolution of many-electron quantum systems is essential for studying dynamical properties in condensed matter, quantum chemistry, and complex materials, yet it poses a significant theoretical and computational challenge. Our work introduces a variational approach for fermionic time-dependent wave functions, surpassing mean-field approximations by accurately capturing many-body correlations. Therefore, we employ time-dependent Jastrow factors and backflow transformations, which are enhanced through neural networks parameterizations. To compute the optimal time-dependent parameters, we utilize the time-dependent variational Monte Carlo technique and a new method based on Taylor-root expansions of the propagator, enhancing the accuracy of our simulations. The approach is demonstrated in three distinct systems. In all cases, we show clear signatures of many-body correlations in the dynamics. The results showcase the ability of our variational approach to accurately capture the time evolution, providing insight into the quantum dynamics of interacting electronic systems, beyond the capabilities of mean-field.

cond-mat.str-el↗

arXiv2024

Variational Benchmarks for Quantum Many-Body Problems

The continued development of computational approaches to many-body ground-state problems in physics and chemistry calls for a consistent way to assess its overall progress. In this work, we introduce a metric of variational accuracy, the V-score, obtained from the variational energy and its variance. We provide an extensive curated dataset of variational calculations of many-body quantum systems, identifying cases where state-of-the-art numerical approaches show limited accuracy, and future algorithms or computational platforms, such as quantum computing, could provide improved accuracy. The V-score can be used as a metric to assess the progress of quantum variational methods toward a quantum advantage for ground-state problems, especially in regimes where classical verifiability is impossible.

quant-ph↗

arXiv2024

Predicting Topological Entanglement Entropy in a Rydberg analog simulator

Predicting the dynamical properties of topological matter is a challenging task, not only in theoretical and experimental settings, but also numerically. This work proposes a variational approach based on a time-dependent correlated Ansatz, focusing on the dynamical preparation of a quantum-spin-liquid state on a Rydberg-atom simulator. Within this framework, we are able to faithfully represent the state of the system throughout the entire dynamical preparation protocol. The flexibility of our approach does not only allow one to match the physically correct form of the Rydberg-atom Hamiltonian but also the relevant lattice topology. This is unlike previous numerical studies which were constrained to simplified versions of the problem through the modification of both the Hamiltonian and the lattice. Our approach further gives access to global quantities such as the topological entanglement entropy ($γ$), providing insight into the topological properties of the system. This is achieved by the introduction of the time-dependent variational Monte Carlo (t-VMC) technique to the dynamics of topologically ordered phases. Upon employing a Jastrow variational Ansatz with a scalable number of parameters, we are able to efficiently extend our simulations to system sizes matching state-of-the-art experiments and beyond. Our results corroborate experimental observations, confirming the presence of topological order during the dynamical state-preparation protocol, and additionally deepen our understanding of topological entanglement dynamics. We show that, while the simulated state exhibits (global) topological order and local properties resembling those of a resonating-valence-bond (RVB) state, it lacks the latter's characteristic topological entanglement entropy signature $γ= \ln(2)$, irrespective of the degree of adiabaticity of the protocol.

quant-ph↗

arXiv2024

Real-time quantum dynamics of thermal states with neural thermofields

Solving the time-dependent quantum many-body Schrödinger equation is a challenging task, especially for states at a finite temperature, where the environment affects the dynamics. Most existing approximating methods are designed to represent static thermal density matrices, 1D systems, and/or zero-temperature states. In this work, we propose a method to study the real-time dynamics of thermal states in two dimensions, based on thermofield dynamics, variational Monte Carlo, and neural-network quantum states. To this aim, we introduce two novel tools: (i) a procedure to accurately simulate the cooling down of arbitrary quantum variational states from infinite temperature, and (ii) a generic thermal (autoregressive) recurrent neural-network (ARNNO) Ansatz that allows for direct sampling from the density matrix using thermofield basis rotations. We apply our technique to the transverse-field Ising model subject to an additional longitudinal field and demonstrate that the time-dependent observables, including correlation operators, can be accurately reproduced for a 4x4 spin lattice. We provide predictions of the real-time dynamics on a 6x6 lattice that lies outside the reach of exact simulations.

quant-ph↗

arXiv2023

Message-Passing Neural Quantum States for the Homogeneous Electron Gas

We introduce a message-passing-neural-network-based wave function Ansatz to simulate extended, strongly interacting fermions in continuous space. Symmetry constraints, such as continuous translation symmetries, can be readily embedded in the model. We demonstrate its accuracy by simulating the ground state of the homogeneous electron gas in three spatial dimensions at different densities and system sizes. With orders of magnitude fewer parameters than state-of-the-art neural-network wave functions, we demonstrate better or comparable ground-state energies. Reducing the parameter complexity allows scaling to $N=128$ electrons, previously inaccessible to neural-network wave functions in continuous space, enabling future work on finite-size extrapolations to the thermodynamic limit. We also show the Ansatz's capability of quantitatively representing different phases of matter.

quant-ph↗