arXiv subjects

Sascha H. Hauck

Publications and source records attributed to Sascha H. Hauck.

6 recordsLinked to original sources

arXiv2026

Performance Benchmarking of Tensor Trains for accelerated Quantum-Inspired Homogenization on TPU, GPU and CPU architectures

Recent advances in high-resolution CT-imaging technology are creating a new class of ultra-high resolved microstructural datasets that challenge the limits of traditional homogenization approaches. While state-of-the-art FFT-based homogenization techniques remain effective for moderate datasets, their memory footprint and computational cost grow rapidly with increasing resolution, making them progressively inefficient for industrial-scale problems. To address these challenges, the recently developed Superfast-Fourier Transform (SFFT)-based homogenization algorithm leverages the memory-efficient low-rank representations of Tensor Trains (TTs), which reduce the storage and computational requirements of large-scale homogenization problems. Developed for CPU usage, SFFT-based Homogenization efficiently handles high-resolution datasets, assuming the underlying data is well-behaved. In this work, we investigate the performance of fundamental TT operations on modern hardware accelerators using the JAX framework. A benchmarking study across CPUs, GPUs, and TPUs evaluates execution times and computational efficiency, highlighting the strengths and limitations of TT operations on different architectures and motivating future hybrid approaches. Building on these insights, we adapt the SFFT-based homogenization algorithm for accelerator execution, enabling homogenization at high resolutions ranging from 300 million to 70 billion grid points, which are infeasible for the best available GPU-based FFT reference implementation. While the observed scaling behavior is geometry-dependent, the results demonstrate the potential of accelerator-based quantum-inspired homogenization for high-performance multiscale simulations.

cond-mat.mtrl-sci↗

arXiv2026

Epigenetic feedback reshapes dynamical landscapes in gene regulatory networks

Understanding how gene regulatory networks (GRNs) give rise to stable and dynamic cellular states remains a central challenge in theoretical biology, particularly when slow epigenetic feedback reshapes the underlying regulatory landscape. While experimental approaches such as single-cell transcriptomics reveal rich dynamical behaviour, a tractable theoretical framework that links gene expression, epigenetic control, and collective dynamics remains challenging. Here, we develop an extended Dynamical Mean Field Theory (DMFT) framework for GRNs that incorporates epigenetic modifications as slow, feedback-driven variables. Building on the analogy between Hopfield networks and spin glass systems, we derive effective stochastic equations that reduce high-dimensional dynamics to a tractable form across multiple timescales. This formulation enables quantitative characterization of both stable and oscillatory regimes and reveals how epigenetic feedback reshapes the effective potential landscape governing cell fate decisions. Our model shows how epigenetic feedback regulation dynamically reshapes the Waddington landscape. Our results and methodology provide a unified theoretical framework for understanding developmental dynamics and epigenetic reprogramming in complex biological systems.

q-bio.MN↗

arXiv2026

Enhanced shortcuts to adiabaticity for coherent atom transport in a family of two-dimensional dynamical optical lattices

In view of the compelling need for coherent atom transport as a prerequisite for a variety of emerging quantum technologies, we investigate such transport on the example of an adjustable family of two-dimensional optical lattices [L. Tarruell {\em et al.}, Nature (London) {\bf 483}, 302 (2012)] that includes square, honeycomb, dimerized, and 1D-chains lattices as its special cases; dynamical optical lattices of this type have already been utilized for the demonstration of topological pumping and the realization of two-qubit quantum gates with neutral atoms. At the outset, we propose the appropriate arrangements of acousto-optic modulators that give rise to a frequency imbalance between counterpropagating laser beams, thus leading to the dynamical-lattice effect in an arbitrary direction in the lattice plane. We subsequently obtain the dynamical-lattice trajectories that enable atom transport in the lattices under consideration using two classes of control schemes: (i) shortcuts to adiabaticity (STA) in the form of inverse engineering based on a dynamical invariant of Lewis-Riesenfeld type, and (ii) their modification, known as enhanced STA (eSTA), which is well-suited for the treatment of anharmonic trapping potentials. We then quantify the resulting atom dynamics using transport fidelities computed from the numerical solutions of the relevant time-dependent Schrödinger equations. By doing so for various choices of the system parameters and transport directions, we demonstrate that -- except in the special case of the dimerized lattice -- the eSTA method consistently outperforms its STA counterpart, both in terms of the achievable transport times and the robustness of the resulting transport against small variations of optical-lattice depths.

quant-ph↗

arXiv2025

SFFT-Based Homogenization: Using Tensor Trains to Enhance FFT-Based Homogenization

Homogenization is a fundamental technique for estimating the macroscopic properties of materials with microscale heterogeneity. Among Homogenization methods, the FFT-based Homogenization algorithm has become widely used due to its computational efficiency and ability to handle complex microstructures. Nevertheless, even with GPU acceleration, FFT-based Homogenization for industrial applications remains excessively time-consuming, particularly when generating elastic training data for AI models. This is due to the curse of dimensionality, which arises from the algorithms reliance on the Fast Fourier Transform, creating a fundamental bottleneck. In this paper, we propose a quantum-inspired SFFT-based Homogenization algorithm that leverages the improved time complexity of a Tensor Train variant of the Quantum Fourier Transform. By additionally exploiting structural properties of the underlying microstructure, our method achieves exponential improvements in time complexity and memory efficiency compared to the traditional FFT-based technique - all while remaining executable on classical hardware. We evaluate the performance of our algorithm across increasingly complex microstructures, demonstrating its potential advantages and limitations.

cond-mat.mtrl-sci↗

arXiv2022

Coherent Atom Transport via Enhanced Shortcuts to Adiabaticity: Double-Well Optical Lattice

Theoretical studies of coherent atom transport have as yet mainly been restricted to one-dimensional model systems with harmonic trapping potentials. Here we investigate this important phenomenon -- a prerequisite for a variety of quantum-technology applications based on cold neutral atoms -- under much more complex physical circumstances. More specificially yet, we study fast atomic transport in a moving {\em double-well optical lattice}, whose three-dimensional (anharmonic) potential is nonseparable in the $x-y$ plane. We first propose specific configurations of acousto-optic modulators that give rise to the moving-lattice effect in an arbitrary direction in this plane. We then determine moving-lattice trajectories that enable single-atom transport using two classes of quantum-control methods: shortcuts to adiabaticity (STA), here utilized in the form of inverse engineering based on a quadratic-in-momentum dynamical invariant of Lewis-Riesenfeld type, and their recently proposed modification termed enhanced STA (eSTA). Subsequently, we quantify the resulting single-atom dynamics by numerically solving the relevant time-dependent Schrödinger equations and compare the efficiency of STA- and eSTA-based transport by evaluating the respective fidelities. We show that -- except for the regime of shallow lattices -- the eSTA method consistently outperforms its STA counterpart. This study has direct implications for neutral-atom quantum computing based on collisional entangling two-qubit gates and quantum sensing of constant homogeneous forces via guided-atom interferometry.

quant-ph↗

arXiv2021

Single-atom transport in optical conveyor belts: Enhanced shortcuts-to-adiabaticity approach

Fast and nearly lossless atomic transport, enabled by moving the confining trap, is a prerequisite for many quantum-technology applications. While theoretical studies of this problem have heretofore focussed almost exclusively on simplified scenarios (one-dimensional systems, purely harmonic confining potentials, etc.), we investigate it here in the experimentally relevant setting of a moving optical lattice ({\em optical conveyor belt}). We model single-atom transport in this system by taking fully into account its three-dimensional, anharmonic confining potential. We do so using the established method of shortcuts to adiabaticity (STA), i.e. an inverse-engineering approach based on Lewis-Riesenfeld invariants, as well as its recently proposed modification known as {\em enhanced} STA (eSTA). By combining well-controlled, advanced analytical techniques and the numerical propagation of a time-dependent Schrödinger equation using the Fourier split operator method, we evaluate atom-transport fidelities within both approaches. Being obtained for realistic choices of system parameters, our results are relevant for future experiments with optical conveyor belts. Moreover, they reveal that in the system at hand the eSTA method outperforms its STA counterpart for all but the lowest optical-lattice depths.

quant-ph↗