Related papers: Kekul\'e Cells for Molecular Computation
Kekul\'e phases are Peierls-like lattice distortions in graphene that are predicted to host novel electronic states beyond graphene (1-8). Although the Kekul\'e phases are realized in graphene through introducing electron-electron…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
Topological states of matter are robust quantum phases, characterised by propagating or localised edge states in an insulating bulk. Topological boundary states can be triggered by various mechanisms, for example by strong spin-orbit…
Individual Kekule valence structures of biphenylene and related hydrocarbons are treated perturbatively by modelling them as sets of weakly-interacting uniform double bonds. Total pi-electron energies of these structures are then expressed…
Recently, a novel GHZ/W graphical calculus has been established to study and reason more intuitively about interacting quantum systems. The compositional structure of this calculus was shown to be well-equipped to sufficiently express…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
Breaking the intrinsic chirality of quasiparticles in graphene enables the emergence of new and intriguing phases. One such paradigmatic example is the bond density wave, which leads to a Kekul\'{e}-ordered structure and underpins exotic…
Round-based models are very common message-passing models; combinatorial topology applied to distributed computing provides sweeping results like general lower bounds. We combine both to study the computability of k-set agreement. Among all…
A spatially non-uniform superconducting phase is proposed as the electronic variational ground state for the attractive interactions between nearest neighbors on graphene's honeycomb lattice, close to and right at the filling one half. The…
A graph is a powerful concept for representation of relations between pairs of entities. Data with underlying graph structure can be found across many disciplines and there is a natural desire for understanding such data better. Deep…
Entanglement is a fundamental resource for many applications in quantum information processing. Here, we investigate how quantum transport in simple quantum graphs, modeled as controlled two-level quantum systems, can be utilized to…
Construction of graphs with equal eigenvalues (co-spectral graphs) is an interesting problem in spectral graph theory. Seidel switching is a well-known method for generating co-spectral graphs. From a matrix theoretic point of view, Seidel…
Introduction: molecular geometry, the three-dimensional arrangement of atoms within a molecule, is fundamental to understanding chemical reactivity, physical properties, and biological activity. The prevailing models used to describe…
Higher-order topological corner states have been realized in two-dimensional Kekul\'{e} lattice, which can be further coupled with spin polarization through the implementation of local magnetization. In this work, we numerically investigate…
This study investigates the topological behavior of a continuous elastic phononic structure characterized by a 3-term Kekul\'e distortion. The elastic waveguide consists of a hexagonal unit cell whose geometric dimensions are intentionally…
Graphene's electronic structure can be fundamentally altered when a substrate- or adatom-induced Kekul\'e superlattice couples the valley and isospin degrees of freedom. Here, we show that the band structure of Kekul\'e-textured graphene…
Recently, several aspects of controlled quantum communication (e.g., bidirectional controlled state teleportation, controlled quantum secure direct communication, controlled quantum dialogue, etc.) have been studied using $n$-qubit…
We theoretically study the competition between two possible exotic superconducting orders that may occur in graphene-like systems, assuming dominant nearest-neighbor attraction: the gapless hidden superconducting order, which renormalizes…
We introduce a generalized Hamiltonian describing not only all topological phases observed experimentally in Kekul\'e graphene (KekGr) but predicting also new ones. These phases show features like a quadratic band crossing point, valley…
In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for…