Related papers: Kekul\'e Cells for Molecular Computation
Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of…
We have measured a graphene double quantum dot device with multiple electrostatic gates that are used to enhance control to investigate it. At low temperatures the transport measurements reveal honeycomb charge stability diagrams which can…
Molecular interactions often involve high-order relationships that cannot be fully captured by traditional graph-based models limited to pairwise connections. Hypergraphs naturally extend graphs by enabling multi-way interactions, making…
Quantum walks have frequently envisioned the behavior of a quantum state traversing a classically defined, generally finite, graph structure. While this approach has already generated significant results, it imposes a strong assumption: all…
Generating and manipulating Dirac points in artificial atomic crystals has received attention especially in photonic systems due to their ease of implementation. In this paper, we propose a two-dimensional photonic crystal made of a…
We examine quantum transport in periodic quantum graphs with a vertex coupling non-invariant with respect to time reversal. It is shown that the graph topology may play a decisive role in the conductivity properties illustrating this claim…
In this paper, we develop SE3Set, an SE(3) equivariant hypergraph neural network architecture tailored for advanced molecular representation learning. Hypergraphs are not merely an extension of traditional graphs; they are pivotal for…
Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of…
The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in…
String diagrams turn algebraic equations into topological moves that have recurring shapes, involving the sliding of one diagram past another. We individuate, at the root of this fact, the dual nature of polygraphs as presentations of…
In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will…
We develop a new general formulation to explore light-driven electron transport through a single-molecule device with multiple pathways. Three individual systems are proposed including (i) a two-terminal molecular junction based on…
We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $C^*$-algebras $B$ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on $L^2(B)$, the quantum…
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…
The rate-equation approach is used to describe sequential tunneling through a molecular junction in the Coulomb blockade regime. Such device is composed of molecular quantum dot (with discrete energy levels) coupled with two metallic…
We consider electronic transport through a single-molecule junction where the molecule has a degenerate spectrum. Unlike previous transport models, and theories a rate-equations description is no longer possible, and the quantum coherences…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
Semiconductor quantum dots provide a two-dimensional analogy for real atoms and show promise for the implementation of scalable quantum computers. Here, we investigate the charge configurations in a silicon metal-oxide-semiconductor double…
Correlations are known to play a crucial role in determining the structure of complex networks. Here we study how their presence affects the computation of the percolation threshold in random hypergraphs. In order to mimic the correlation…
Electronic transport across n-Si-alkyl monolayer/Hg junctions is, at reverse and low forward bias, independent of alkyl chain-length from 18 down to 1 or 2 carbons! This and further recent results indicate that electron transport is…