arXiv subjects

Patrick Holzer

Publications and source records attributed to Patrick Holzer.

6 recordsLinked to original sources

arXiv2026

Benchmarking Encoding Families in Quantum Neural Networks Under Fixed Circuit Area for Frequency Spectrum and Trainability

Quantum Neural Networks (QNNs) offer a promising framework for integrating quantum computing principles into machine learning, yet their practical capabilities and limitations remain insufficiently studied. In this work, we systematically investigate the trainability and approximation properties of QNNs by benchmarking diverse circuit architectures and encoding strategies across synthetic and real-world datasets. We analyze several ans\"atze, including Hamming, binary, exponential, ternary, turnpike and Golomb, by evaluating their ability to learn synthetic data modeled as random finite Fourier series. To assess real-world applicability, we further evaluate QNNs on two time-series classification tasks: a Fischertechnik pneumatic leak detection dataset and the publicly available NASA bearing fault dataset. Our experiments show that while broader frequency spectra can theoretically enhance expressivity, practical trainability is strongly influenced by architectural factors such as qubit count and circuit depth. Notably, we find that QNNs perform best when the frequency spectrum is tailored to the target function's complexity but remains as compact as possible. Moreover, architectures with identical frequency spectra can differ in trainability, with configurations using more qubits and fewer layers generally performing better, except in the single-layer case. These findings provide guidelines for selecting QNN ans\"atze and offer new insights into the interplay between expressivity and trainability in quantum machine learning.

quant-ph↗

arXiv2024

Application of ZX-calculus to Quantum Architecture Search

This paper presents a novel approach to quantum architecture search by integrating the techniques of ZX-calculus with Genetic Programming (GP) to optimize the structure of parameterized quantum circuits employed in Quantum Machine Learning (QML). Recognizing the challenges in designing efficient quantum circuits for QML, we propose a GP framework that utilizes mutations defined via ZX-calculus, a graphical language that can simplify visualizing and working with quantum circuits. Our methodology focuses on evolving quantum circuits with the aim of enhancing their capability to approximate functions relevant in various machine learning tasks. We introduce several mutation operators inspired by the transformation rules of ZX-calculus and investigate their impact on the learning efficiency and accuracy of quantum circuits. The empirical analysis involves a comparative study where these mutations are applied to a diverse set of quantum regression problems, measuring performance metrics such as the percentage of valid circuits after the mutation, improvement of the objective, as well as circuit depth and width. Our results indicate that certain ZX-calculus-based mutations perform significantly better than others for Quantum Architecture Search (QAS) in all metrics considered. They suggest that ZX-diagram based QAS results in shallower circuits and more uniformly allocated gates than crude genetic optimization based on the circuit model.

quant-ph↗

arXiv2024

Spectral invariance and maximality properties of the frequency spectrum of quantum neural networks

We analyze the frequency spectrum of Quantum Neural Networks (QNNs) using Minkowski sums, which yields a compact algebraic description and permits explicit computation. Using this description, we prove several maximality results for broad classes of QNN architectures. Under some mild technical conditions we establish a bijection between classes of models with the same area $A:=R\cdot L$ that preserves the frequency spectrum, where $R$ denotes the number of qubits and $L$ the number of layers, which we consequently call spectral invariance under area-preserving transformations. With this we explain the symmetry in $R$ and $L$ in the results often observed in the literature and show that the maximal frequency spectrum depends only on the area $A=RL$ and not on the individual values of $R$ and $L$. Moreover, we collect and extend existing results and specify the maximum possible frequency spectrum of a QNN with an arbitrary number of layers as a function of the spectrum of its generators. In the case of arbitrary dimensional generators, where our two introduced notions of maximality differ, we extend existing Golomb ruler based results and introduce a second novel approach based on a variation of the turnpike problem, which we call the relaxed turnpike problem. We clarify comprehensively how the generators of a QNN must be chosen in order to obtain a maximal frequency spectrum for a given area $A$, thereby contributing to a deeper theoretical understanding. However, our numerical experiments show that trainability depends not only on $A = RL$, but also on the choice of $(R,L)$, so that knowledge of the maximum frequency spectrum alone is not sufficient to ensure good trainability.

quant-ph↗

arXiv2023

Dynamically Weighted Federated k-Means

Federated clustering, an integral aspect of federated machine learning, enables multiple data sources to collaboratively cluster their data, maintaining decentralization and preserving privacy. In this paper, we introduce a novel federated clustering algorithm named Dynamically Weighted Federated k-means (DWF k-means) based on Lloyd's method for k-means clustering, to address the challenges associated with distributed data sources and heterogeneous data. Our proposed algorithm combines the benefits of traditional clustering techniques with the privacy and scalability benefits offered by federated learning. The algorithm facilitates collaborative clustering among multiple data owners, allowing them to cluster their local data collectively while exchanging minimal information with the central coordinator. The algorithm optimizes the clustering process by adaptively aggregating cluster assignments and centroids from each data source, thereby learning a global clustering solution that reflects the collective knowledge of the entire federated network. We address the issue of empty clusters, which commonly arises in the context of federated clustering. We conduct experiments on multiple datasets and data distribution settings to evaluate the performance of our algorithm in terms of clustering score, accuracy, and v-measure. The results demonstrate that our approach can match the performance of the centralized classical k-means baseline, and outperform existing federated clustering methods like k-FED in realistic scenarios.

cs.LG↗

arXiv2022

A Quantum Computing Approach for the Unit Commitment Problem

Planning energy production is a challenging task due to its cost-sensitivity, fast-moving energy markets, uncertainties in demand, and technical constraints of power plants. Thus, more complex models of this so-called \emph{unit commitment problem (UCP)} have to be solved more rapidly, a task that probably can be solved more efficiently via quantum computing. In this article, we model a UCP with minimum running and idle times as a quadratic unconstrained optimization problem to solve it on quantum computing hardware. First experiments confirm the advantages of our formulation in terms of qubit usage and connectivity and most importantly solution quality.

quant-ph↗

arXiv2022

Fed-DART and FACT: A solution for Federated Learning in a production environment

Federated Learning as a decentralized artificial intelligence (AI) solution solves a variety of problems in industrial applications. It enables a continuously self-improving AI, which can be deployed everywhere at the edge. However, bringing AI to production for generating a real business impact is a challenging task. Especially in the case of Federated Learning, expertise and resources from multiple domains are required to realize its full potential. Having this in mind we have developed an innovative Federated Learning framework FACT based on Fed-DART, enabling an easy and scalable deployment, helping the user to fully leverage the potential of their private and decentralized data.

cs.LG↗