相关论文: Kekul\'e Cells for Molecular Computation
Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps…
Simulating percolation and critical phenomena of labelled species inside films composed of single-component linear homogeneous macromolecules using molecular Monte Carlo method in 3 dimensions, we study dependence of these conducting…
Geometric deep learning (GDL) has demonstrated huge power and enormous potential in molecular data analysis. However, a great challenge still remains for highly efficient molecular representations. Currently, covalent-bond-based molecular…
Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…
We investigate a graph-theoretic approach to the problem of distinguishing quantum product states in the fundamental quantum communication framework called local operations and classical communication (LOCC). We identify chordality as the…
It is well-known that maximally entangled states such as the Greenberger-Horne-Zeilinger (GHZ) states, with the Bell states as the simplest examples, are widely exploited in quantum information and computation. We study the application of…
In this manuscript we analyse generalised port-based teleportation (PBT) schemes, allowing for transmitting more than one unknown quantum state (or a composite quantum state) in one go, where the state ends up in several ports at Bob's…
An edge subset $S$ of a connected graph $G$ is called an anti-Kekul\'{e} set if $G-S$ is connected and has no perfect matching. We can see that a connected graph $G$ has no anti-Kekul\'{e} set if and only if each spanning tree of $G$ has a…
Complex networks are the representative graphs of interactions in many complex systems. Usually, these interactions are abstractions of the communication/diffusion channels between the units of the system. Real complex networks, e.g.…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
An alternative foundation for 2-categories is explored by studying graph-theoretically a partial operation on 2-cells named juncture, which can replace vertical and horizontal composition. Juncture is a generalized vertical composition of…
Recent advances have led towards first prototypes of quantum networks in which entanglement is distributed by sources producing bipartite entangled states. This raises the question of which states can be generated in quantum networks based…
Molecular representation is a critical element in our understanding of the physical world and the foundation for modern molecular machine learning. Previous molecular machine learning models have employed strings, fingerprints, global…
In this paper the authors extend [1] and provide more details of how the brain may act like a quantum computer. In particular, positing the difference between voltages on two axons as the environment for ions undergoing spatial…
A new type of disorder-driven electronic percolation transition is found for two-dimensional electron gas (2DEG), based on a quantum cellular automaton model. This transition is shown to be accompanied with a metal-insulator transition, as…
We analytically explore the scaling properties of a general class of nested subgraphs in complex networks, which includes the $K$-core and the $K$-scaffold, among others. We name such class of subgraphs $K$-nested subgraphs due to the fact…
We study the band gap in some semi-conducting polymers with two models: H\"uckel molecular orbital theory and the so-called free electron model. The two models are directly related to spectral theory on combinatorial and metric graphs.
Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…
We consider the problem of online graph multi-coloring with advice. Multi-coloring is often used to model frequency allocation in cellular networks. We give several nearly tight upper and lower bounds for the most standard topologies of…
We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated coloured tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams…