arXiv subjects

Katharina Ludwig

Publications and source records attributed to Katharina Ludwig.

9 recordsLinked to original sources

arXiv2026

YZ-plane measurement-based quantum computation: Universality and Parity Architecture implementation

We define the class of register-logic graphs and prove that any uniformly deterministic measurement-based quantum computation (MBQC) where the inputs coincide with the outputs must be driven on such graphs by measurements in the $YZ$ plane of the Bloch sphere. This observation is revisited in the context that goes beyond uniform determinism, where we present a universal $YZ$-plane-only measurement pattern and establish a connection between $YZ$-plane-only and $XZ$-plane-only patterns. These results conclude the line of research on universal patterns with measurements restricted to one of the principal planes of the Bloch sphere. We further demonstrate, within the framework of the Parity Architecture, that $YZ$-plane patterns with the register-logic graph can be embedded into another graph with purely local interactions, and we extend this case to the scenario of universal quantum computation.

quant-ph↗

arXiv2026

SWAP-less Implementation of Quantum Algorithms

We present a formalism based on tracking the flow of parity quantum information to implement algorithms on devices with limited connectivity without qubit overhead, SWAP operations or shuttling. Instead, we leverage the fact that entangling gates not only manipulate quantum states but can also be exploited to transport quantum information. We demonstrate the effectiveness of this method by applying it to the quantum Fourier transform (QFT) and the Quantum Approximate Optimization Algorithm (QAOA) with $n$ qubits. This improves upon all state-of-the-art implementations of the QFT on a linear nearest-neighbor architecture, resulting in a total circuit depth of ${5n-3}$ and requiring ${n^2-1}$ CNOT gates. For the QAOA, our method outperforms SWAP networks, which are currently the most efficient implementation of the QAOA on a linear architecture. We further demonstrate the potential to balance qubit count against circuit depth by implementing the QAOA on twice the number of qubits using bi-linear connectivity, which approximately halves the circuit depth.

quant-ph↗

arXiv2026

The Parity Flow Formalism: Tracking Quantum Information Throughout Computation

We propose the Parity Flow formalism, a method for tracking the information flow in quantum circuits. This method adds labels to quantum circuit diagrams such that the action of Clifford gates can be understood as a recoding of quantum information. The action of non-Clifford gates in the encoded space can be directly deduced from those labels without backtracking. An application of flow tracking is to design resource-efficient quantum circuits by changing any present encoding via a simple set of rules. Finally, the Parity Flow formalism can be used in combination with stabilizer codes to further reduce quantum circuit depth and to reveal additional operations that can be implemented in parallel.

quant-ph↗

arXiv2023

NeMig -- A Bilingual News Collection and Knowledge Graph about Migration

News recommendation plays a critical role in shaping the public's worldviews through the way in which it filters and disseminates information about different topics. Given the crucial impact that media plays in opinion formation, especially for sensitive topics, understanding the effects of personalized recommendation beyond accuracy has become essential in today's digital society. In this work, we present NeMig, a bilingual news collection on the topic of migration, and corresponding rich user data. In comparison to existing news recommendation datasets, which comprise a large variety of monolingual news, NeMig covers articles on a single controversial topic, published in both Germany and the US. We annotate the sentiment polarization of the articles and the political leanings of the media outlets, in addition to extracting subtopics and named entities disambiguated through Wikidata. These features can be used to analyze the effects of algorithmic news curation beyond accuracy-based performance, such as recommender biases and the creation of filter bubbles. We construct domain-specific knowledge graphs from the news text and metadata, thus encoding knowledge-level connections between articles. Importantly, while existing datasets include only click behavior, we collect user socio-demographic and political information in addition to explicit click feedback. We demonstrate the utility of NeMig through experiments on the tasks of news recommenders benchmarking, analysis of biases in recommenders, and news trends analysis. NeMig aims to provide a useful resource for the news recommendation community and to foster interdisciplinary research into the multidimensional effects of algorithmic news curation.

cs.IR↗

arXiv2022

Towards Analyzing the Bias of News Recommender Systems Using Sentiment and Stance Detection

News recommender systems are used by online news providers to alleviate information overload and to provide personalized content to users. However, algorithmic news curation has been hypothesized to create filter bubbles and to intensify users' selective exposure, potentially increasing their vulnerability to polarized opinions and fake news. In this paper, we show how information on news items' stance and sentiment can be utilized to analyze and quantify the extent to which recommender systems suffer from biases. To that end, we have annotated a German news corpus on the topic of migration using stance detection and sentiment analysis. In an experimental evaluation with four different recommender systems, our results show a slight tendency of all four models for recommending articles with negative sentiments and stances against the topic of refugees and migration. Moreover, we observed a positive correlation between the sentiment and stance bias of the text-based recommenders and the preexisting user bias, which indicates that these systems amplify users' opinions and decrease the diversity of recommended news. The knowledge-aware model appears to be the least prone to such biases, at the cost of predictive accuracy.

cs.IR↗

arXiv2015

The Kodaira dimension of the moduli space of Prym varieties

We study the enumerative geometry of the moduli space R_g of Prym varieties of dimension g-1 (also known as the space of admissible double covers). Our main result is that the compactification of R_g is of general type as soon as g>13. We achieve this by computing the class of two types of cycles on R_g: one defined in terms of Koszul cohomology of Prym curves, the other defined in terms of Raynaud theta divisors associated to certain vector bundles on curves. We formulate a Prym-Green conjecture on syzygies of Prym-canonical curves. In the appendix we show that even though R_g has non-canonical singularities, pluricanonical forms on R_g extend to any desingularization.

math.AG↗

arXiv2011

Wave chaos in the non-equilibrium dynamics of the Gross-Pitaevskii equation

The Gross-Pitaevskii equation (GPE) plays an important role in the description of Bose-Einstein condensates (BECs) at the mean-field level. The GPE belongs to the class of non-linear Schrödinger equations which are known to feature dynamical instability and collapse for attractive non-linear interactions. We show that the GPE with repulsive non-linear interactions typical for BECs features chaotic wave dynamics. We find positive Lyapunov exponents for BECs expanding in periodic and aperiodic smooth external potentials as well as disorder potentials. Our analysis demonstrates that wave chaos characterized by the exponential divergence of nearby initial wavefunctions is to be distinguished from the notion of non-integrability of non-linear wave equations. We discuss the implications of these observations for the limits of applicability of the GPE, the problem of Anderson localization, and the properties of the underlying many-body dynamics.

cond-mat.quant-gas↗

arXiv2007

On the geometry of the moduli space of spin curves

We determine the smooth locus and the locus of canonical singularities in the Cornalba compactification \bar S_g of the moduli space S_g of spin curves, i.e., smooth curves of genus g with a theta characteristic. Moreover, the following lifting result for pluricanonical forms is proved: Every pluricanonical form on the smooth locus of \bar S_g extends holomorphically to a desingularisation of \bar S_g.

math.AG↗

arXiv2004

A new family of rational surfaces in P^4

We describe a new method of constructing rational surfaces with given invariants in P^4 and present a family of degree 11 rational surfaces of sectional genus 11 with 2 six-secants that we found with this method.

math.AG↗