Related papers: Spectra of Perfect State Transfer Hamiltonians on …
We examine conditions for a pair of strongly cospectral vertices to have pretty good quantum state transfer in terms of minimal polynomials, and provide cases where pretty good state transfer can be ruled out. We also provide new examples…
A set of Pauli stings is well characterized by the graph that encodes its commutatitivity structure, i.e., by its frustration graph. This graph provides a natural interface between graph theory and quantum information, which we explore in…
Transferring quantum states efficiently between distant nodes of an information processing circuit is of paramount importance for scalable quantum computing. We report on the first observation of a perfect state transfer protocol on a…
We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the…
In this paper we study spectral properties of adjacency and Laplace operators on percolation subgraphs of Cayley graphs of amenable, finitely generated groups. In particular we describe the asymptotic behaviour of the integrated density of…
We study scattering for continuous-time quantum walks on finite graphs with two attached leads. We derive explicit formulae for the two-terminal scattering matrix in terms of characteristic polynomials of the finite graph and its…
Fractals, a fascinating mathematical concept made popular in the eighties, remained for decades a beautiful scientific curiosity mainly. With the tremendous advances in nanofabrication techniques, such as nanolithography, it has become…
We describe a protocol for perfectly transferring a quantum state from one party to another under the dynamics of a fixed, engineered Hamiltonian. Our protocol combines the concepts of fractional revival, dual rail encoding, and a rare…
We study a transport phenomenon in certain coined quantum walks where a subspace of states localized at a vertex gets transferred to another vertex. We first develop characterizations for perfect and pretty good subspace state transfer…
We study quantum state transfer through a qubit network modeled by spins with XY interaction, when relying on a single excitation. We show that it is possible to achieve perfect transfer by shifting (adding) energy to specific vertices.…
In this paper, we study the Hamiltonicity of graphs with large minimum degree. Firstly, we present some conditions for a simple graph to be Hamilton-connected and traceable from every vertex in terms of the spectral radius of the graph or…
Let $G$ be a graph with adjacency matrix $A$. The transition matrix corresponding to $G$ is defined by $H(t):=\exp{\left(itA\right)}$, $t\in\Rl$. The graph $G$ is said to have perfect state transfer (PST) from a vertex $u$ to another vertex…
Quantum state transfer, first introduced by Bose in 2003, is an important physical phenomenon in quantum networks, which plays a vital role in quantum communication and quantum computing. In 2004, Christandl et al. proposed the concept of…
We quantify the effect of weighted loops at the source and target nodes of a graph on the strength of quantum state transfer between these vertices. We give lower bounds on loop weights that guarantee strong transfer fidelity that works for…
A uniformly coupled double quantum Hamiltonian for a spin chain has recently been implemented experimentally. We propose a method for the determination of initial quantum states that will provide perfect or near-perfect state transmission…
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…
We study quantum-state transfer in $XX$ spin-$1/2$ chains where both communicating spins are weakly coupled to a channel featuring disordered on-site magnetic fields. Fluctuations are modelled by long-range correlated sequences with…
We consider the quantum site percolation model on graphs with an amenable group action. It consists of a random family of Hamiltonians. Basic spectral properties of these operators are derived: non-randomness of the spectrum and its…
We show how to achieve perfect quantum state transfer and construct effective two-qubit gates between distant sites in engineered bosonic and fermionic networks. The Hamiltonian for the system can be determined by choosing an eigenvalue…
We establish the theory for pretty good state transfer in discrete-time quantum walks. For a class of walks, we show that pretty good state transfer is characterized by the spectrum of certain Hermitian adjacency matrix of the graph; more…