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Sophia Keip

Publications and source records attributed to Sophia Keip.

5 recordsLinked to original sources
arXiv2025

Exploring the Varchenko Determinant of Partial Cubes

The Varchenko matrix is known to have a well-structured determinant for complexes of oriented matroids (COMs). COMs can be characterized as partial cubes that do not have certain forbidden pc-minors. In this work, we generalize the Varchenko matrix and its determinant to partial cubes. We identify examples of partial cubes whose Varchenko determinants lack a clean factorization, as well as those that exhibit such a structure. These findings open the door for further research into the properties and potential characterizations of partial cubes with well-behaved Varchenko determinants.

math.CO↗
arXiv2025

QCLAB: A Matlab Toolbox for Quantum Computing

We introduce QCLAB, an object-oriented MATLAB toolbox for constructing, representing, and simulating quantum circuits. Designed with an emphasis on numerical stability, efficiency, and performance, QCLAB provides a reliable platform for prototyping and testing quantum algorithms. For advanced performance needs, QCLAB++ serves as a complementary C++ package optimized for GPU-accelerated quantum circuit simulations. Together, QCLAB and QCLAB++ form a comprehensive toolkit, balancing the simplicity of MATLAB scripting with the computational power of GPU acceleration. This paper serves as an introduction to the package and its features along with a hands-on tutorial that invites researchers to explore its capabilities right away.

quant-ph↗
arXiv2024

The Chain Matrix of Bouquets of Geometric Lattices and its Determinant

This work builds on Varchenko et al's introduction of bilinear forms for hyperplane arrangements, where the determinant of the associated matrices factorizes into simple components. While one of the determinant formula developed by Varchenko has been generalized to complexes of oriented matroids (COMs) already, this question was open for another, distinct form. Motivated by work from Varchenko and Brylawski, who generalized the alternative bilinear form and its determinant formula from hyperplane arrangements to matroids, we examine whether this formula can similarly be generalized to COMs. Our findings affirm this generalization, and we further extend the determinant formula to bouquets of geometric lattices as introduced by Laurent et al.

math.CO↗
arXiv2022

Kirchberger's Theorem for Complexes of Oriented Matroids

The separation theorem of Kirchberger can be proven using a combination of Farkas' Lemma and Caratheodory's Theorem. Since those theorems are at the heart of oriented matroids, we are interested in a generalization of Kirchberger's Theorem to them. This has already been done for rank 3 oriented matroids. Here we prove it for complexes of oriented matroids, which are a generalization of oriented matroids.

math.CO↗