arXiv subjects

Robert Schade

Publications and source records attributed to Robert Schade.

16 recordsLinked to original sources

arXiv2026

Reducing the Complexity of Density-Matrix Functionals in a Real-Space-Decomposed DF+RDMF Scheme with the Adaptive Cluster Approximation

Reduced density-matrix functional theory (RDMFT) provides a variational route to electronic correlations beyond conventional density-functional approximations, but explicit evaluations of density-matrix functionals still scale exponentially with the number of active one-particle states. We formulate and assess a real-space-decomposed density-functional plus reduced-density-matrix-functional (DF+RDMF) scheme in which the Coulomb interaction is partitioned locally in real space and the RDMF correction is evaluated only for the strongly correlated part of the interaction. The resulting local density-matrix functionals are further compressed using the adaptive cluster approximation (ACA), which performs a unitary rotation of the bath subspace before truncation and therefore preserves the local interaction while reducing the number of explicitly correlated bath states. As a molecular test case, we consider the bending potential of carbon suboxide, C$_3$O$_2$. While semilocal PBE favors a linear molecule, the DF+RDMF/ACA correction stabilizes a bent configuration in qualitative agreement with the quasilinear behavior inferred from spectroscopy. The approach provides a systematic embedding hierarchy for combining density functionals with explicitly correlated density-matrix corrections in extended or spatially inhomogeneous systems.

physics.chem-ph↗

arXiv2026

The CP-PAW code package for first-principles calculations from a user's perspective

CP-PAW is a combined electronic structure and ab-initio molecular dynamics code to perform mixed quantum and classical simulations of atomistic condensed phase systems, such as solids, liquids, and molecular systems. As the name suggests, the CP-PAW code unifies the all-electron projector augmented-wave method with the Car-Parrinello approach to determine not only the electronic and nuclear ground state of condensed matter, but also to study their properties and dynamics. In addition to briefly outlining the underlying theory, the focus will be on unique aspects of CP-PAW and how to correctly employ them as a user. How to install CP-PAW using the new build system will also be briefly mentioned.

cond-mat.mtrl-sci↗

arXiv2025

Otus Supercomputer

Otus is a high-performance computing cluster that was launched in 2025 and is operated by the Paderborn Center for Parallel Computing (PC2) at Paderborn University in Germany. The system is part of the National High Performance Computing (NHR) initiative. Otus complements the previous supercomputer Noctua 2, offering approximately twice the computing power while retaining the three node types that were characteristic of Noctua 2: 1) CPU compute nodes with different memory capacities, 2) high-end GPU nodes, and 3) HPC-grade FPGA nodes. On the Top500 list, which ranks the 500 most powerful supercomputers in the world, Otus is in position 164 with the CPU partition and in position 255 with the GPU partition (June 2025). On the Green500 list, ranking the 500 most energy-efficient supercomputers in the world, Otus is in position 5 with the GPU partition (June 2025). This article provides a comprehensive overview of the system in terms of its hardware, software, system integration, and its overall integration into the data center building to ensure energy-efficient operation. The article aims to provide unique insights for scientists using the system and for other centers operating HPC clusters. The article will be continuously updated to reflect the latest system setup and measurements.

cs.DC↗

arXiv2025

The CP2K Program Package Made Simple

CP2K is a versatile open-source software package for simulations across a wide range of atomistic systems, from isolated molecules in the gas phase to low-dimensional functional materials and interfaces, as well as highly symmetric crystalline solids, disordered amorphous glasses, and weakly interacting soft-matter systems in the liquid state and in solution. This review highlights CP2K's capabilities for computing both static and dynamical properties using quantum-mechanical and classical simulation methods. In contrast to the accompanying theory and code paper [J. Chem. Phys. 152, 194103 (2020)], the focus here is on the practical usage and applications of CP2K, with underlying theoretical concepts introduced only as needed.

physics.comp-ph↗

arXiv2024

PHOENIX -- Paderborn highly optimized and energy efficient solver for two-dimensional nonlinear Schr\"odinger equations with integrated extensions

In this work, we introduce PHOENIX, a highly optimized explicit open-source solver for two-dimensional nonlinear Schr\"odinger equations with extensions. The nonlinear Schr\"odinger equation and its extensions (Gross-Pitaevskii equation) are widely studied to model and analyze complex phenomena in fields such as optics, condensed matter physics, fluid dynamics, and plasma physics. It serves as a powerful tool for understanding nonlinear wave dynamics, soliton formation, and the interplay between nonlinearity, dispersion, and diffraction. By extending the nonlinear Schr\"odinger equation, various physical effects such as non-Hermiticity, spin-orbit interaction, and quantum optical aspects can be incorporated. PHOENIX is designed to accommodate a wide range of applications by a straightforward extendability without the need for user knowledge of computing architectures or performance optimization. The high performance and power efficiency of PHOENIX are demonstrated on a wide range of entry-class to high-end consumer and high-performance computing GPUs and CPUs. Compared to a more conventional MATLAB implementation, a speedup of up to three orders of magnitude and energy savings of up to 99.8% are achieved. The performance is compared to a performance model showing that PHOENIX performs close to the relevant performance bounds in many situations. The possibilities of PHOENIX are demonstrated with a range of practical examples from the realm of nonlinear (quantum) photonics in planar microresonators with active media including exciton-polariton condensates. Examples range from solutions on very large grids, the use of local optimization algorithms, to Monte Carlo ensemble evolutions with quantum noise enabling the tomography of the system's quantum state.

physics.comp-ph↗

arXiv2024

Scalable quantum detector tomography by high-performance computing

At large scales, quantum systems may become advantageous over their classical counterparts at performing certain tasks. Developing tools to analyse these systems at the relevant scales, in a manner consistent with quantum mechanics, is therefore critical to benchmarking performance and characterising their operation. While classical computational approaches cannot perform like-for-like computations of quantum systems beyond a certain scale, classical high-performance computing (HPC) may nevertheless be useful for precisely these characterisation and certification tasks. By developing open-source customised algorithms using high-performance computing, we perform quantum tomography on a megascale quantum photonic detector covering a Hilbert space of $10^6$. This requires finding $10^8$ elements of the matrix corresponding to the positive operator valued measure (POVM), the quantum description of the detector, and is achieved in minutes of computation time. Moreover, by exploiting the structure of the problem, we achieve highly efficient parallel scaling, paving the way for quantum objects up to a system size of $10^{12}$ elements to be reconstructed using this method. In general, this shows that a consistent quantum mechanical description of quantum phenomena is applicable at everyday scales. More concretely, this enables the reconstruction of large-scale quantum sources, processes and detectors used in computation and sampling tasks, which may be necessary to prove their nonclassical character or quantum computational advantage.

quant-ph↗

arXiv2023

Computing and Compressing Electron Repulsion Integrals on FPGAs

The computation of electron repulsion integrals (ERIs) over Gaussian-type orbitals (GTOs) is a challenging problem in quantum-mechanics-based atomistic simulations. In practical simulations, several trillions of ERIs may have to be computed for every time step. In this work, we investigate FPGAs as accelerators for the ERI computation. We use template parameters, here within the Intel oneAPI tool flow, to create customized designs for 256 different ERI quartet classes, based on their orbitals. To maximize data reuse, all intermediates are buffered in FPGA on-chip memory with customized layout. The pre-calculation of intermediates also helps to overcome data dependencies caused by multi-dimensional recurrence relations. The involved loop structures are partially or even fully unrolled for high throughput of FPGA kernels. Furthermore, a lossy compression algorithm utilizing arbitrary bitwidth integers is integrated in the FPGA kernels. To our best knowledge, this is the first work on ERI computation on FPGAs that supports more than just the single most basic quartet class. Also, the integration of ERI computation and compression it a novelty that is not even covered by CPU or GPU libraries so far. Our evaluation shows that using 16-bit integer for the ERI compression, the fastest FPGA kernels exceed the performance of 10 GERIS ($10 \times 10^9$ ERIs per second) on one Intel Stratix 10 GX 2800 FPGA, with maximum absolute errors around $10^{-7}$ - $10^{-5}$ Hartree. The measured throughput can be accurately explained by a performance model. The FPGA kernels deployed on 2 FPGAs outperform similar computations using the widely used libint reference on a two-socket server with 40 Xeon Gold 6148 CPU cores of the same process technology by factors up to 6.0x and on a new two-socket server with 128 EPYC 7713 CPU cores by up to 1.9x.

cs.AR↗

arXiv2022

Roadmap on Electronic Structure Codes in the Exascale Era

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing.

cond-mat.mtrl-sci↗

arXiv2022

Parallel Quantum Chemistry on Noisy Intermediate-Scale Quantum Computers

A novel parallel hybrid quantum-classical algorithm for the solution of the quantum-chemical ground-state energy problem on gate-based quantum computers is presented. This approach is based on the reduced density-matrix functional theory (RDMFT) formulation of the electronic structure problem. For that purpose, the density-matrix functional of the full system is decomposed into an indirectly coupled sum of density-matrix functionals for all its subsystems using the adaptive cluster approximation to RDMFT. The approximations involved in the decomposition and the adaptive cluster approximation itself can be systematically converged to the exact result. The solutions for the density-matrix functionals of the effective subsystems involves a constrained minimization over many-particle states that are approximated by parametrized trial states on the quantum computer similarly to the variational quantum eigensolver. The independence of the density-matrix functionals of the effective subsystems introduces a new level of parallelization and allows for the computational treatment of much larger molecules on a quantum computer with a given qubit count. In addition, for the proposed algorithm techniques are presented to reduce the qubit count, the number of quantum programs, as well as its depth. The new approach is demonstrated for Hubbard-like systems on IBM quantum computers based on superconducting transmon qubits.

quant-ph↗

arXiv2022

Breaking the Exascale Barrier for the Electronic Structure Problem in Ab-Initio Molecular Dynamics

The non-orthogonal local submatrix method applied to electronic-structure based molecular dynamics simulations is shown to exceed 1.1 EFLOP/s in FP16/FP32 mixed floating-point arithmetic when using 4,400 NVIDIA A100 GPUs of the Perlmutter system. This is enabled by a modification of the original method that pushes the sustained fraction of the peak performance to about 80%. Example calculations are performed for SARS-CoV-2 spike proteins with up to 83 million atoms.

physics.comp-ph↗

arXiv2022

CP2K on the road to exascale

The CP2K program package, which can be considered as the swiss army knife of atomistic simulations, is presented with a special emphasis on ab-initio molecular dynamics using the second-generation Car-Parrinello method. After outlining current and near-term development efforts with regards to massively parallel low-scaling post-Hartree-Fock and eigenvalue solvers, novel approaches on how we plan to take full advantage of future low-precision hardware architectures are introduced. Our focus here is on combining our submatrix method with the approximate computing paradigm to address the immanent exascale era.

cond-mat.mtrl-sci↗

arXiv2022

Towards Electronic Structure-Based Ab-Initio Molecular Dynamics Simulations with Hundreds of Millions of Atoms

We push the boundaries of electronic structure-based \textit{ab-initio} molecular dynamics (AIMD) beyond 100 million atoms. This scale is otherwise barely reachable with classical force-field methods or novel neural network and machine learning potentials. We achieve this breakthrough by combining innovations in linear-scaling AIMD, efficient and approximate sparse linear algebra, low and mixed-precision floating-point computation on GPUs, and a compensation scheme for the errors introduced by numerical approximations. The core of our work is the non-orthogonalized local submatrix method (NOLSM), which scales very favorably to massively parallel computing systems and translates large sparse matrix operations into highly parallel, dense matrix operations that are ideally suited to hardware accelerators. We demonstrate that the NOLSM method, which is at the center point of each AIMD step, is able to achieve a sustained performance of 324 PFLOP/s in mixed FP16/FP32 precision corresponding to an efficiency of 67.7% when running on 1536 NVIDIA A100 GPUs.

physics.comp-ph↗

arXiv2020

A Submatrix-Based Method for Approximate Matrix Function Evaluation in the Quantum Chemistry Code CP2K

Electronic structure calculations based on density-functional theory (DFT) represent a significant part of today's HPC workloads and pose high demands on high-performance computing resources. To perform these quantum-mechanical DFT calculations on complex large-scale systems, so-called linear scaling methods instead of conventional cubic scaling methods are required. In this work, we take up the idea of the submatrix method and apply it to the DFT computations in the software package CP2K. For that purpose, we transform the underlying numeric operations on distributed, large, sparse matrices into computations on local, much smaller and nearly dense matrices. This allows us to exploit the full floating-point performance of modern CPUs and to make use of dedicated accelerator hardware, where performance has been limited by memory bandwidth before. We demonstrate both functionality and performance of our implementation and show how it can be accelerated with GPUs and FPGAs.

physics.comp-ph↗

arXiv2020

CP2K: An Electronic Structure and Molecular Dynamics Software Package -- Quickstep: Efficient and Accurate Electronic Structure Calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular and biological systems. It is especially aimed at massively-parallel and linear-scaling electronic structure methods and state-of-the-art ab-initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2k to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

physics.chem-ph↗

arXiv2018

Adaptive cluster approximation for reduced density-matrix functional theory

A method, called the adaptive cluster approximation (ACA), for single-impurity Anderson models is proposed. It is based on reduced density-matrix functional theory, where the one-particle reduced density matrix is used as the basic variable. The adaptive cluster approximation introduces a unitary transformation of the bath states such that the effect of the bath is concentrated to a small cluster around the impurity. For this small effective system one can then either calculate the reduced density-matrix functional numerically exact from Levy's constrained-search formalism or approximate it by an implicit approximation of the reduced density-matrix functional. The method is evaluated for single-impurity Anderson models with finite baths. The method converges rapidly to the exact result with the size of the effective bath.

cond-mat.str-el↗

arXiv2016

Reduced density-matrix functionals applied to the Hubbard dimer

Common density-matrix functionals, the Müller and the power functional, have been benchmarked for the half-filled Hubbard dimer, which allows to model the bond dissociation problem and the transition from the weakly to the strongly correlated limit. Unbiased numerical calculations are combined with analytical results. Despite the well known successes of the Müller functional, the ground state is degenerate with a one-dimensional manifold of ferromagnetic solutions. The resulting infinite magnetic susceptibility indicates another qualitative flaw of Müller's functional. The derivative discontinuity with respect to particle number is not present indicating an incorrect metal-like behavior. The power functional actually favors the ferromagnetic state for weak interaction. Analogous to the Hartree-Fock approximation, the power functional undergoes a transition beyond a critical interaction strength, in this case however, to a non-collinear antiferromagnetic state.

cond-mat.str-el↗