On subfields of the Hermitian function fields involving the involution automorphism

A function field over a finite field is called maximal if it achieves the Hasse-Weil bound. Finding possible genera that maximal function fields achieve has both theoretical interest and practical applications to coding theory and other topics. As a subfield of a maximal function field is also maximal, one way to find maximal function fields is to find all subfields of a maximal function field. Due to the large automorphism group of the Hermitian function field, it is natural to find as many subfields of the Hermitian function field as possible. In literature, most of papers studied subfields fixed by subgroups of the decomposition group at one point (usually the point at infinity). This is because it becomes much more complicated to study the subfield fixed by a subgroup that is not contained in the decomposition group at one point. In this paper, we study subfields of the Hermitian function field fixed by subgroups that are not contained in the decomposition group of any point except the cyclic subgroups. It turns out that some new maximal function fields are found

Provable learning of quantum states with graphical models

The complete learning of an $n$-qubit quantum state requires samples exponentially in $n$. Several works consider subclasses of quantum states that can be learned in polynomial sample complexity such as stabilizer states or high-temperature Gibbs states. Other works consider a weaker sense of learning, such as PAC learning and shadow tomography. In this work, we consider learning states that are close to neural network quantum states, which can efficiently be represented by a graphical model called restricted Boltzmann machines (RBMs). To this end, we exhibit robustness results for efficient provable two-hop neighborhood learning algorithms for ferromagnetic and locally consistent RBMs. We consider the $L_p$-norm as a measure of closeness, including both total variation distance and max-norm distance in the limit. Our results allow certain quantum states to be learned with a sample complexity \textit{exponentially} better than naive tomography. We hence provide new classes of efficiently learnable quantum states and apply new strategies to learn them

On the Way to SBOMs: Investigating Design Issues and Solutions in Practice

Software Bill of Materials (SBOM), offers improved transparency and supply chain security by providing a machine-readable inventory of software components used. With the rise in software supply chain attacks, the SBOM has attracted attention from both academia and industry. This paper presents a study on the practice of SBOM, based on the analysis of 4,786 GitHub discussions from 510 SBOM-related projects. Our study identifies key topics, challenges, and solutions associated with effective SBOM usage. We also highlight commonly used tools and frameworks for generating SBOMs, along with their respective strengths and limitations. Our research underscores the importance of SBOMs in software development and the need for their widespread adoption to enhance supply chain security. Additionally, the insights gained from our study can inform future research and development in this field