531 research outputs found
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 -qubit quantum state requires samples
exponentially in . 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 -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
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