Related papers: The Cheeger constant of a quantum graph
Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are…
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
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…
Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a…
As a non-trivial extension of the celebrated Cheeger inequality, the higher-order Cheeger inequalities for graphs due to Lee, Oveis Gharan and Trevisan provide for each $k$ an upper bound for the $k$-way Cheeger constant in forms of…
The quantum circuit model is the default for encoding an algorithm intended for a NISQ computer or a quantum computing simulator. A simple graph and through it, a graph state - quantum state physically manifesting an abstract graph…
A major application of the mathematical concept of graph in quantum mechanics is to model networks of electrical wires or electromagnetic wave-guides. In this paper, we address the dynamics of a particle trapped on such a network in…
Given a known or unknown phase encoded in a higher-dimensional qudit gate, it is possible to send copies of a gate that encodes the phase to multiple receivers based on a generalized quantum teleportation. We extend this quantum gate…
Quantum Chromodynamics is an established part of the Standard Model and an essential part of the toolkit for searching for new physics at high-energy colliders. I present a status report on the theory of QCD and review some of the important…
The symmetric tensor power of graphs is introduced and its fundamental properties are explored. A wide range of intriguing phenomena occur when one considers symmetric tensor powers of familiar graphs. A host of open questions are…
Statistical properties of evolving random graphs are analyzed using kinetic theory. Treating the linking process dynamically, structural characteristics such as links, paths, cycles, and components are obtained analytically using the rate…
We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…
The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in…
This work explores the spectra of quantum graphs where the Schr\"odinger operator on the edges is equipped with a potential. The scattering approach, which was originally introduced for the potential free case, is extended to this case and…
Quantum entanglement plays a crucial role in quantum computing. Entangling information has important implications for understanding the behavior of quantum programs and avoiding entanglement-induced errors. Entanglement analysis is a static…
In this article we develop a graphical calculus for stable invariants of Riemannian manifolds akin to the graphical calculus for Rozansky-Witten invariants for hyperk\"ahler manifolds; based on interpreting trivalent graphs with colored…
We introduce a notion of curvature on finite, combinatorial graphs. It can be easily computed by solving a linear system of equations. We show that graphs with curvature bounded below by $K>0$ have diameter bounded by $\mbox{diam}(G) \leq…
We study how quantum walks can be used to find structural anomalies in graphs via several examples. Two of our examples are based on star graphs, graphs with a single central vertex to which the other vertices, which we call external…
In this paper we study the quantum wave packet of the Schrodinger equation for continuous quantum measurements.
We consider branched quantum wires, whose connection rules provide PT-symmetry for the Schrodinger equation on graph. For such PT-symmetric quantum graph we derive general boundary conditions which keep the Hamiltonian as PT-symmetric with…