Related papers: Kekul\'e Cells for Molecular Computation
Aspects of cell metabolism are modeled by ordinary differential equations describing the change of intracellular chemical concentrations. There is a correspondence between this dynamical system and a complex network. As in the classic…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
The anti-Kekul\'{e} number of a connected graph $G$ is the smallest number of edges whose deletion results in a connected subgraph having no Kekul\'{e} structures (perfect matchings). As a common generalization of (conditional) matching…
This work provides a complete description of entanglement properties between electrons inside coupled quantum molecules, nanoestructures which consist of two quantum dots. Each electron can tunnel between the two quantum dots inside the…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
We construct infinite families of graphs in which pretty good state transfer can be induced by adding a potential to the nodes of the graph (i.e. adding a number to a diagonal entry of the adjacency matrix). Indeed, we show that given any…
Quantum networks are composed of nodes which can send and receive quantum states by exchanging photons. Their goal is to facilitate quantum communication between any nodes, something which can be used to send secret messages in a secure…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…
Quantum computing is a unique computational approach that promises tremendous performance that cannot be achieved by classical computers, although several problems must be resolved to realize a practical quantum computing system for easy…
Formation of a molecular network from multifunctional precursors is modelled with a random graph process. The random graph model favours reactivity for monomers that are positioned close in the network topology, and disfavours reactivity…
The present paper is concerned with the concept of the one-way quantum computer, beyond binary-systems, and its relation to the concept of stabilizer quantum codes. This relation is exploited to analyze a particular class of quantum…
Quantum computation can be formulated through various models, each highlighting distinct structural and resource-theoretic aspects of quantum computational power. This paper develops a unified categorical framework that encompasses these…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
We study the percolation properties of graph partitioning on random regular graphs with N vertices of degree $k$. Optimal graph partitioning is directly related to optimal attack and immunization of complex networks. We find that for any…
The exchange graph of a cluster algebra encodes the combinatorics of mutations of clusters. Through the recent "categorifications" of cluster algebras using representation theory one obtains a whole variety of exchange graphs associated…
We investigate the dynamical properties of quasiparticles in graphene superlattices with three typical Kekul\'{e} distortions (i.e., Kekul\'{e}-O, Kekul\'{e}-Y and Kekul\'{e}-M). On the one hand, we numerically show the visualized evolution…
Using density-functional theory, we calculate the electronic bandstructure of single-layer graphene on top of hexagonal In_2Te_2 monolayers. The geometric configuration with In and Te atoms at centers of carbon hexagons leads to a Kekule'…
We propose to use a new platform - ultracold polar molecules - for quantum computing with switchable interactions. The on/off switch is accomplished by selective excitation of one of the "0" or "1" qubits - long-lived molecular states - to…
This work studies how a suitably-designed classical system generates with a quantum-like (QL) state space mediated by a graph. The graph plays a special dual role by directing the topology of the classical network and defining a state space…