Related papers: Boundary condition at the junction
We consider quantum search on graphs. Recently, it has been shown that the graph properties like connectivity, global symmetry, or regularity cannot serve as a reliable criteria that must be satisfied by a graph to allow a successful…
Many computational problems are unchanged under some symmetry operation. In classical machine learning, this can be reflected with the layer structure of the neural network. In quantum machine learning, the ansatz can be tuned to correspond…
Graphical Models have various applications in science and engineering which include physics, bioinformatics, telecommunication and etc. Usage of graphical models needs complex computations in order to evaluation of marginal functions,so…
Boundary conditions strongly affect the results of numerical computations for finite size inhomogeneous or incommensurate structures. We present a method which allows to deal with this problem, both for ground state and for critical…
The practical utility of a quantum network depends on its ability to establish entanglement between arbitrary node pairs with quality sufficient to execute entanglement enabled tasks. This capability can be assessed globally, through…
We consider the dynamics on a quantum graph as the limit of the dynamics generated by a one-particle Hamiltonian in R^2 with a potential having a deep strict minimum on the graph, when the width of the well shrinks to zero. For a generic…
Quantum Graphity is an approach to quantum gravity based on a background independent formulation of condensed matter systems on graphs. We summarize recent results obtained on the notion of emergent geometry from the point of view of a…
The purpose of this article is to explore the properties of integrable, purely transmitting, defects placed at the junctions of several one-dimensional domains within a network. The defect sewing conditions turn out to be quite restrictive…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…
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 quantum association schemes. This allows to define distance regular and strongly regular quantum graphs. We bring examples thereof. In addition, we formulate the duality for translation quantum association schemes corresponding…
The approach to equilibrium of quantum mechanical systems is a topic as old as quantum mechanics itself, but has recently seen a surge of interest due to applications in quantum technologies, including, but not limited to, quantum…
We present a stack model for breaking down the complexity of entanglement-based quantum networks. More specifically, we focus on the structures and architectures of quantum networks and not on concrete physical implementations of network…
In this paper, we discuss the concept of quantum graphs with transparent vertices by considering the case where the graph interacts with an external time-independent field. In particular, we address the problem of transparent boundary…
Steady technological advances are paving the way for the implementation of the quantum internet, a network of locations interconnected by quantum channels. Here we propose a model to simulate a quantum internet based on optical fibers and…
We review the theory of Cheeger constants for graphs and quantum graphs and their present and envisaged applications.
We prove an analog of Krein's resolvent formula expressing the resolvents of self-adjoint extensions in terms of boundary conditions. Applications to quantum graphs and systems with point interactions are discussed.
Quantum networks play a major role in long-distance communication, quantum cryptography, clock synchronization, and distributed quantum computing. Generally, these protocols involve many independent sources sharing entanglement among…
An exactly solved bosonic tunneling model is studied along a line of the coupling parameter space, which includes a quantum phase boundary line. The entire energy spectrum is computed analytically, and found to exhibit multiple energy level…
We consider the motion by mean curvature of an $n$-dimensional graph over a time-dependent domain in $\mathbb{R}^n$, intersecting $\mathbb{R}^n$ at a constant angle. In the general case, we prove local existence for the corresponding…