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Thomas Eckl

Publications and source records attributed to Thomas Eckl.

At least 19 recordsLinked to original sources
arXiv2026

The Future of Computing for Materials Science Challenges

Materials discovery increasingly relies on the coordinated use of theory, computation, experiment, data-driven methods, and emerging quantum technologies, yet the full potential of these tools is realised only when they operate within workflows that reflect the complexity of real systems. This perspective summarises current capabilities, limitations, and opportunities across these domains, drawing on contributions from academia, industry, and national laboratories to identify the scientific and structural requirements for more reliable and efficient discovery. Classical simulations provide broad coverage across design spaces, while experimental measurements reveal degradation, heterogeneity, and kinetic processes that determine performance under realistic conditions. Machine learning accelerates exploration when supported by well-curated datasets with clear provenance and uncertainty quantification, and quantum computing offers promising routes into correlated electronic behaviour when aligned with properties that influence engineering decisions. Collectively, these insights highlight the need for reproducible workflows, shared data standards, realistic benchmarks, and a research culture that prepares scientists to work across paradigms. By integrating these methodological and organisational elements, the community can move toward discovery processes that deliver robust predictions, support confident decision making, and shorten the path from conceptual design to deployable materials.

cond-mat.mtrl-sci↗
arXiv2026

Grothendieck's Equality vs Voevodsky's Equality

We discuss how canonical and universal constructions, properties and characterizations interact with equality in the framework of Homotopy Type Theory, comparing it with Grothendieck's use of equality and shedding further light on (efficient) formalisation of mathematics. This is achieved by investigating examples that range from monoids, groups, rings and modules to cohomology theories in the category of modules over commutative rings and culminate in a cohomological criterion of flatness.

math.LO↗
arXiv2024

Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions.

quant-ph↗
arXiv2024

OnionVQE Optimization Strategy for Ground State Preparation on NISQ Devices

The Variational Quantum Eigensolver (VQE) is one of the most promising and widely used algorithms for exploiting the capabilities of current Noisy Intermediate-Scale Quantum (NISQ) devices. However, VQE algorithms suffer from a plethora of issues, such as barren plateaus, local minima, quantum hardware noise, and limited qubit connectivity, thus posing challenges for their successful deployment on hardware and simulators. In this work, we propose a VQE optimization strategy that builds upon recent advances in the literature, and exhibits very shallow circuit depths when applied to the specific system of interest, namely a model Hamiltonian representing a cuprate superconductor. These features make our approach a favorable candidate for generating good ground state approximations on current NISQ devices. Our findings illustrate the potential of VQE algorithmic development for leveraging the full capabilities of NISQ devices.

quant-ph↗
arXiv2024

Dynamical Mean Field Theory for Real Materials on a Quantum Computer

Quantum computers (QC) could harbor the potential to significantly advance materials simulations, particularly at the atomistic scale involving strongly correlated fermionic systems where an accurate description of quantum many-body effects scales unfavorably with size. While a full-scale treatment of condensed matter systems with currently available noisy quantum computers remains elusive, quantum embedding schemes like dynamical mean-field theory (DMFT) allow the mapping of an effective, reduced subspace Hamiltonian to available devices to improve the accuracy of ab initio calculations such as density functional theory (DFT). Here, we report on the development of a hybrid quantum-classical DFT+DMFT simulation framework which relies on a quantum impurity solver based on the Lehmann representation of the impurity Green's function. Hardware experiments with up to 14 qubits on the IBM Quantum system are conducted, using advanced error mitigation methods and a novel calibration scheme for an improved zero-noise extrapolation to effectively reduce adverse effects from inherent noise on current quantum devices. We showcase the utility of our quantum DFT+DMFT workflow by assessing the correlation effects on the electronic structure of a real material, Ca2CuO2Cl2, and by carefully benchmarking our quantum results with respect to exact reference solutions and experimental spectroscopy measurements.

cond-mat.str-el↗
arXiv2022

Extending the Variational Quantum Eigensolver to Finite Temperatures

We present a variational quantum thermalizer (VQT), called quantum-VQT (qVQT), which extends the variational quantum eigensolver (VQE) to finite temperatures. The qVQT makes use of an intermediate measurement between two variational circuits to encode a density matrix on a quantum device. A classical optimization provides the thermal state and, simultaneously, all associated excited states of a quantum mechanical system. We demonstrate the capabilities of the qVQT for two different spin systems. First, we analyze the performance of qVQT as a function of the circuit depth and the temperature for a 1-dimensional Heisenberg chain. Second, we use the excited states to map the complete, temperature dependent phase diagram of a 2-dimensional J1-J2 Heisenberg model. The numerical experiments demonstrate the efficiency of our approach, which can be readily applied to study various quantum many-body systems at finite temperatures on currently available NISQ devices.

quant-ph↗
arXiv2022

Effects of thermal, elastic, and surface properties on the stability of SiC polytypes

SiC polytypes have been studied for decades, both experimentally and with atomistic simulations, yet no consensus has been reached on the factors that determine their stability and growth. Proposed governing factors are temperature-dependent differences in the bulk energy, biaxial strain induced through point defects, and surface properties. In this work, we investigate the thermodynamic stability of the 3C, 2H, 4H, and 6H polytypes with density functional theory (DFT) calculations. The small differences of the bulk energies between the polytypes can lead to intricate changes in their energetic ordering depending on the computational method. Therefore, we employ and compare various DFT-codes: VASP, CP2K, and FHI-aims; exchange-correlation functionals: LDA, PBE, PBEsol, PW91, HSE06, SCAN, and RTPSS; and nine different van der Waals (vdW) corrections. At $T=0$~K, 4H-SiC is marginally more stable than 3C-SiC, and the stability further increases with temperature by including entropic effects from lattice vibrations. Neither the most advanced vdW corrections nor strain on the lattice have a significant effect on the relative polytype stability. We further investigate the energies of the (0001) polytype surfaces that are commonly exposed during epitaxial growth. For Si-terminated surfaces, we find 3C-SiC to be significantly more stable than 4H-SiC. We conclude that the difference in surface energy is likely the driving force for 3C-nucleation, whereas the difference in the bulk thermodynamic stability slightly favors the 4H and 6H polytypes. In order to describe the polytype stability during crystal growth correctly, it is thus crucial to take into account both of these effects.

cond-mat.mtrl-sci↗
arXiv2020

Observation of separated dynamics of charge and spin in the Fermi-Hubbard model

Strongly correlated quantum systems give rise to many exotic physical phenomena, including high-temperature superconductivity. Simulating these systems on quantum computers may avoid the prohibitively high computational cost incurred in classical approaches. However, systematic errors and decoherence effects presented in current quantum devices make it difficult to achieve this. Here, we simulate the dynamics of the one-dimensional Fermi-Hubbard model using 16 qubits on a digital superconducting quantum processor. We observe separations in the spreading velocities of charge and spin densities in the highly excited regime, a regime that is beyond the conventional quasiparticle picture. To minimize systematic errors, we introduce an accurate gate calibration procedure that is fast enough to capture temporal drifts of the gate parameters. We also employ a sequence of error-mitigation techniques to reduce decoherence effects and residual systematic errors. These procedures allow us to simulate the time evolution of the model faithfully despite having over 600 two-qubit gates in our circuits. Our experiment charts a path to practical quantum simulation of strongly correlated phenomena using available quantum devices.

quant-ph↗
arXiv2020

Preparing symmetry broken ground states with variational quantum algorithms

One of the most promising applications for near term quantum computers is the simulation of physical quantum systems, particularly many-electron systems in chemistry and condensed matter physics. In solid state physics, finding the correct symmetry broken ground state of an interacting electron system is one of the central challenges. The Variational Hamiltonian Ansatz (VHA), a variational hybrid quantum-classical algorithm especially suited for finding the ground state of a solid state system, will in general not prepare a broken symmetry state unless the initial state is chosen to exhibit the correct symmetry. In this work, we discuss three variations of the VHA designed to find the correct broken symmetry states close to a transition point between different orders. As a test case we use the two-dimensional Hubbard model where we break the symmetry explicitly by means of external fields coupling to the Hamiltonian and calculate the response to these fields. For the calculation we simulate a gate-based quantum computer and also consider the effects of dephasing noise on the algorithms. We find that two of the three algorithms are in good agreement with the exact solution for the considered parameter range. The third algorithm agrees with the exact solution only for a part of the parameter regime, but is more robust with respect to dephasing compared to the other two algorithms.

quant-ph↗
arXiv2018

Effective birational rigidity of Fano double hypersurfaces

We prove birational superrigidity of Fano double hypersurfaces of index one with quadratic and multi-quadratic singularities, satisfying certain regularity conditions, and give an effective explicit lower bound for the codimension of the set of non-rigid varieties in the natural parameter space of the family. The lower bound is quadratic in the dimension of the variety. The proof is based on the techniques of hypertangent divisors combined with the recently discovered $4n^2$-inequality for complete intersection singularities.

math.AG↗
arXiv2017

Crystallographic Tilings

Crystallographic tilings of the Euclidean space $\mathbb{E}^n$ are defined as simple tilings whose group of isometric automorphisms is crystallographic. To classify crystallographic tilings by their automorphism groups it is necessary to extend the standard equivalence relation of mutual local derivability to a version taking more general isometries than translations into account. This also requires the extension of the standard metrics on tiling spaces. Finally, a tiling with a given crystallographic group as automorphism group is constructed.

math.DS↗
arXiv2017

Topological equivalence of holomorphic foliation germs of rank $1$ with isolated singularity in the Poincaré domain

We show that the topological equivalence class of holomorphic foliation germs with an isolated singularity of Poincaré type is determined by the topological equivalence class of the real intersection foliation of the (suitably normalized) foliation germ with a sphere centered in the singularity. We use this Reconstruction Theorem to completely classify topological equivalence classes of plane holomorphic foliation germs of Poincaré type and discuss a conjecture on the classification in dimension $\geq 3$.

math.CV↗
arXiv2016

Numerical analogues of the Kodaira dimension and the Abundance Conjecture

We add further notions to Lehmann's list of numerical analogues to the Kodaira dimension of pseudo-effective divisors on smooth complex projective varieties, and show new relations between them. Then we use these notions and relations to fill in a gap in Lehmann's arguments, thus proving that most of these notions are equal. Finally, we show that the Abundance Conjecture, as formulated in the context of the Minimal Model Program, and the Generalized Abundance Conjecture using these numerical analogues to the Kodaira dimension, are equivalent for non-uniruled complex projective varieties.

math.AG↗
arXiv2015

Iterative dissection of Okounkov bodies of graded linear series on $\mathbb{CP}^2$

Let $π: X \rightarrow \mathbb{P}^2$ be the blow-up of $\mathbb{CP}^2$ in $n$ points $x_i$ in very general position, and let $E_i$ be the exceptional divisor over $x_i$. For $0 \leq n \leq 9$ we calculate Okounkov bodies of graded linear series given by sections of multiples of line bundles $π^\ast \mathcal{O}_{\mathbb{P}^2}(d) \otimes \mathcal{O}_X(-m\sum_{i=1}^n E_i)$ with respect to a flag consisting of a line on $\mathbb{CP}^2$ and a point on the line in general position. Furthermore, we show what Nagata's Conjecture predicts on these Okounkov bodies when $n > 9$.

math.AG↗
arXiv2014

On the global log canonical threshold of Fano complete intersections

We show that the global log canonical threshold of generic Fano complete intersections of index 1 and codimension $k$ in ${\mathbb P}^{M+k}$ is equal to 1 if $M\geqslant 3k+4$ and the highest degree of defining equations is at least 8. This improves the earlier result where the inequality $M\geqslant 4k+1$ was required, so the class of Fano complete intersections covered by our theorem is considerably larger. The theorem implies, in particular, that the Fano complete intersections satisfying our assumptions admit a K\" ahler-Einstein metric. We also show the existence of K\" ahler-Einstein metrics for a new finite set of families of Fano complete intersections.

math.AG↗
arXiv2012

On the locus of non-rigid hypersurfaces

We show that the Zariski closure of the set of hypersurfaces of degree $M$ in ${\mathbb P}^{M}$, where $M\geq 5$, which are either not factorial or not birationally superrigid, is of codimension at least $\binom{M-3}{2}+1$ in the parameter space.

math.AG↗
arXiv2009

Ciliberto-Miranda degenerations of $\mathbb{CP}^2$ blown up in 10 points

We simplify Ciliberto's and Miranda's method(arXiv:0812.0032) to construct degenerations of $\mathbb{CP}^2$ blown up in several points yielding lower bounds of the corresponding multi-point Seshadri constants. In particular we exploit an asymptotic result of the author (arXiv:math/0508561) which allows to check the non-specialty of much fewer linear systems on $\mathbb{CP}^2$. We obtain the lower bound 117/370 for the 10-point Seshadri constant on $\mathbb{CP}^2$.

math.AG↗