Related papers: On quantum graph filters with flat passbands
We demonstrate that a quantum graph exhibits a $\mathcal{PT}$-symmetry provided the coefficients in the condition describing the wave function matching at the vertices are circulant matrices; this symmetry is nontrivial if they are not…
Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting…
We explore algebraic and spectral properties of weighted graphs containing twin vertices that are useful in quantum state transfer. We extend the notion of adjacency strong cospectrality to arbitrary Hermitian matrices, with focus on the…
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…
A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix…
We investigate a periodic quantum graph in form of a square lattice with a general self-adjoint coupling at the vertices. We analyze the spectrum, in particular, its high-energy behaviour. Depending on the coupling type, bands and gaps have…
This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals…
We consider a quantum mechanical particle living on a graph and discuss the behaviour of its wavefunction at graph vertices. In addition to the standard (or delta type) boundary conditions with continuous wavefunctions, we investigate two…
A blow-up of $n$ copies of a graph $G$ is the graph $\overset{n}\uplus~G$ obtained by replacing every vertex of $G$ by an independent set of size $n$, where the copies of vertices in $G$ are adjacent in the blow-up if and only if the…
Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…
Electron transmission through different gated and gapped graphene superlattices (GSLs) is studied. Linear, Gaussian, Lorentzian and P\"oschl-Teller superlattice potential profiles have been assessed. A relativistic description of electrons…
We discuss the basic problem of signal transmission in quantum mechanics in terms of topological theories. Using the analogy between knot diagrams and quantum amplitudes we calculate the transmission coefficients of the concept topological…
Quantum graphs with leads to infinity serve as convenient models for studying various aspects of systems which are usually attributed to chaotic scattering. They are also studied in several experimental systems and practical applications.…
We explore the tunneling behavior of a quantum particle on a finite graph, in the presence of an asymptotically large potential. Surprisingly the behavior is governed by the local symmetry of the graph around the wells.
We theoretically analyse the possibility to electrostatically confine electrons in circular quantum dot arrays, impressed on contacted graphene nanoribbons by top gates. Utilising exact numerical techniques, we compute the scattering…
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…
We show evidence of the backscattering of quantum Hall edge channels in a narrow graphene Hall bar, induced by the gating effect of the conducting tip of a Scanning Gate Microscope, which we can position with nanometer precision. We show…
We consider a typical circuit QED setup where an artificial atom encodes a qubit and is dispersively coupled to a measurement resonator that in turn is coupled to a transmission line. We show theoretically that by placing another artificial…
Microwave transmission line spectroscopy is used to observe the integer quantum Hall effect in two samples of monolayer graphene with different geometries that are resistively-coupled to a coplanar waveguide. We find plateaus in transmitted…
Certain lattice wave systems in translationally invariant settings have one or more spectral bands that are strictly flat or independent of momentum in the tight binding approximation, arising from either internal symmetries or fine-tuned…