arXiv subjects

Holger Eble

Publications and source records attributed to Holger Eble.

8 recordsLinked to original sources

arXiv2025

Blockchain Network Analysis using Quantum Inspired Graph Neural Networks & Ensemble Models

In the rapidly evolving domain of financial technology, the detection of illicit transactions within blockchain networks remains a critical challenge, necessitating robust and innovative solutions. This work proposes a novel approach by combining Quantum Inspired Graph Neural Networks (QI-GNN) with flexibility of choice of an Ensemble Model using QBoost or a classic model such as Random Forrest Classifier. This system is tailored specifically for blockchain network analysis in anti-money laundering (AML) efforts. Our methodology to design this system incorporates a novel component, a Canonical Polyadic (CP) decomposition layer within the graph neural network framework, enhancing its capability to process and analyze complex data structures efficiently. Our technical approach has undergone rigorous evaluation against classical machine learning implementations, achieving an F2 score of 74.8% in detecting fraudulent transactions. These results highlight the potential of quantum-inspired techniques, supplemented by the structural advancements of the CP layer, to not only match but potentially exceed traditional methods in complex network analysis for financial security. The findings advocate for a broader adoption and further exploration of quantum-inspired algorithms within the financial sector to effectively combat fraud.

cs.LG↗

arXiv2024

Introducing the Kernel Descent Optimizer for Variational Quantum Algorithms

In recent years, variational quantum algorithms have garnered significant attention as a candidate approach for near-term quantum advantage using noisy intermediate-scale quantum (NISQ) devices. In this article we introduce kernel descent, a novel algorithm for minimizing the functions underlying variational quantum algorithms. We compare kernel descent to existing methods and carry out extensive experiments to demonstrate its effectiveness. In particular, we showcase scenarios in which kernel descent outperforms gradient descent and quantum analytic descent. The algorithm follows the well-established scheme of iteratively computing classical local approximations to the objective function and subsequently executing several classical optimization steps with respect to the former. Kernel descent sets itself apart with its employment of reproducing kernel Hilbert space techniques in the construction of the local approximations, which leads to the observed advantages.

quant-ph↗

arXiv2024

Denoising Gradient Descent in Variational Quantum Algorithms

In this article we introduce an algorithm for mitigating the adverse effects of noise on gradient descent in variational quantum algorithms. This is accomplished by computing a {\emph{regularized}} local classical approximation to the objective function at every gradient descent step. The computational overhead of our algorithm is entirely classical, i.e., the number of circuit evaluations is exactly the same as when carrying out gradient descent using the parameter-shift rules. We empirically demonstrate the advantages offered by our algorithm on randomized parametrized quantum circuits.

quant-ph↗

arXiv2023

Interpolating Parametrized Quantum Circuits using Blackbox Queries

This article focuses on developing classical surrogates for parametrized quantum circuits using interpolation via (trigonometric) polynomials. We develop two algorithms for the construction of such surrogates and prove performance guarantees. The constructions are based on circuit evaluations which are blackbox in the sense that no structural specifics of the circuits are exploited. While acknowledging the limitations of the blackbox approach compared to whitebox evaluations, which exploit specific circuit properties, we demonstrate scenarios in which the blackbox approach might prove beneficial. Sample applications include but are not restricted to the approximation of VQEs and the alleviaton of the barren plateau problem.

quant-ph↗

arXiv2022

The MST-fan of a regular subdivision

The dual graph $Γ(h)$ of a regular triangulation $Σ(h)$ carries a natural metric structure. The minimum spanning trees of $Γ(h)$ recently proved to be conclusive for detecting significant data signal in the context of population genetics. In this paper we prove that the parameter space of such minimum spanning trees is organized as a polyhedral fan, called the MST-fan of $Σ(h)$, which subdivides the secondary cone of $Σ(h)$ into parameter cones. We partially describe its local face structure and examine the connection to tropical geometry in virtue of matroids and Bergman fans.

math.CO↗

arXiv2021

Computing characteristic polynomials of hyperplane arrangements with symmetries

We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers of an arrangement as a byproduct of computing its characteristic polynomial. We showcase our julia implementation, based on OSCAR, on examples coming from hyperplane arrangements with applications to physics and computer science.

math.CO↗

arXiv2020

Master regulators of evolution and the microbiome in higher dimensions

A longstanding goal of biology is to identify the key genes and species that critically impact evolution, ecology, and health. Network analysis has revealed keystone species that regulate ecosystems and master regulators that regulate cellular genetic networks. Yet these studies have focused on pairwise biological interactions, which can be affected by the context of genetic background and other species present generating higher-order interactions. The important regulators of higher-order interactions are unstudied. To address this, we applied a new high-dimensional geometry approach that quantifies epistasis in a fitness landscape to ask how individual genes and species influence the interactions in the rest of the biological network. We then generated and also reanalyzed 5-dimensional datasets (two genetic, two microbiome). We identified key genes (e.g. the rbs locus and pykF) and species (e.g. Lactobacilli) that control the interactions of many other genes and species. These higher-order master regulators can induce or suppress evolutionary and ecological diversification by controlling the topography of the fitness landscape. Thus, we provide mathematical intuition and justification for exploration of biological networks in higher dimensions.

q-bio.QM↗

arXiv2019

Cluster partitions and fitness landscapes of the Drosophila fly microbiome

Beerenwinkel et al.(2007) suggested studying fitness landscapes via regular subdivisions of convex polytopes. Building on their approach we propose cluster partitions and cluster filtrations of fitness landscapes as a new mathematical tool. In this way, we provide a concise combinatorial way of processing metric information from epistatic interactions. Using existing Drosophila microbiome data, we demonstrate similarities with and differences to the previous approach. As one outcome we locate interesting epistatic information where the previous approach is less conclusive.

q-bio.QM↗