arXiv subjects

Maximilian Lutz

Publications and source records attributed to Maximilian Lutz.

3 recordsLinked to original sources

arXiv2026

Adiabatic quantum state preparation in integrable models

We propose applying the adiabatic algorithm to prepare high-energy eigenstates of integrable models on a quantum computer. We first review the standard adiabatic algorithm to prepare ground states in each magnetization sector of the prototypical XXZ Heisenberg chain. Based on the thermodynamic Bethe ansatz, we show that the algorithm circuit depth is polynomial in the number of qubits $N$, outperforming previous methods explicitly relying on integrability. Next, we propose a protocol to prepare arbitrary eigenstates of integrable models that satisfy certain conditions. For a given target eigenstate, we construct a suitable parent Hamiltonian written in terms of a complete set of local conserved quantities. We propose using such Hamiltonian as an input for an adiabatic algorithm. After benchmarking this construction in the case of the non-interacting XY spin chain, where we can rigorously prove its efficiency, we apply it to prepare arbitrary eigenstates of the Richardson-Gaudin models. In this case, we provide numerical evidence that the circuit depth of our algorithm is polynomial in $N$ for all eigenstates, despite the models being interacting.

quant-ph↗

arXiv2025

Towards personalised assessment of abdominal aortic aneurysm structural integrity

Abdominal aortic aneurysm (AAA) is a life-threatening condition characterized by the progressive dilation of the aorta, which can lead to rupture if undetected or untreated. Stress-based rupture risk estimation using computational biomechanics has been widely studied; however, it requires wall strength data that cannot be measured in humans in vivo. To overcome this limitation, the goal of this study is to present a new method for biomechanical assessment of AAA via simultaneous consideration of tension and strain in AAA wall. We present a patient-specific, non-invasive method for assessing the structural integrity of the AAA wall using only time-resolved 3D computed tomography angiography (4D-CTA) images and blood pressure data. The proposed approach integrates wall strain (throughout the cardiac cycle) and wall tension analysis to compute a novel index, the Relative Structural Integrity Index (RSII), which quantifies local wall stiffness independently of wall thickness, wall material properties, and blood pressure measurement conditions. We applied our method to twenty patients from three different hospitals to extract visual RSII maps over the AAA wall of each individual patient and to compare the RSII values between aneurysmal and non-aneurysmal aortas in one patient. Our results primarily show similar RSII values across all patients, indicating the consistency of the method. Additionally, we observed patterns consistent with experimental findings reported in the literature: AAA walls exhibited higher stiffness than healthy aortic walls, while localized low-stiffness zones in the AAA wall were predominantly found in the most dilated regions.

cs.CE↗

arXiv2025

Towards Full Automation of Geometry Extraction for Biomechanical Analysis of Abdominal Aortic Aneurysm; Neural Network-Based versus Classical Methodologies

Background: For the clinical adoption of stress-based rupture risk estimation in abdominal aortic aneurysms (AAAs), a fully automated pipeline, from clinical imaging to biomechanical stress computation, is essential. To this end, we investigated the impact of AI-based image segmentation methods on stress computation results in the walls of AAAs. We compared wall stress distributions and magnitudes calculated from geometry models obtained from classical semi-automated segmentation versus automated neural network-based segmentation. Method: 16 different AAA contrast-enhanced computed tomography (CT) images were semi-automatically segmented by an analyst, taking between 15 and 40 minutes of human effort per patient, depending on image quality. The same images were automatically segmented using PRAEVAorta2 commercial software by NUREA (https://www.nurea-soft.com/), developed based on artificial intelligence (AI) algorithms, and automatically post-processed with an in-house MATLAB code, requiring only 1-2 minutes of computer time per patient. Aneurysm wall stress calculations were automatically performed using the BioPARR software (https://bioparr.mech.uwa.edu.au/). Results: Compared to the classical semi-automated segmentation, the automatic neural network-based segmentation leads to equivalent stress distributions, and slightly higher peak and 99th percentile maximum principal stress values. However, our statistical analysis indicated that the differences in AAA wall stress obtained using the two segmentation methods are not statistically significant and fall well within the typical range of inter-analyst and intra-analyst variability. Conclusions: Our findings are a steppingstone toward a fully automated pipeline for biomechanical analysis of AAAs, starting with CT scans and concluding with wall stress assessment.

cs.CE↗