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A quantum random walk model is established on a one-dimensional periodic lattice that fluctuates between two possible states. This model is defined by Lindblad rate equations that incorporate the transition rates between the two lattice…
Effective transport of quantum information is an essential element of quantum computation. We consider the problem of transporting a quantum state by using a moving potential well, while maintaining the encoded quantum information. In…
Quantum state transfer in a triangular domain of a two-dimensional, equally-spaced, spin lat- tice with non-homogeneous nearest-neighbor couplings is analyzed. An exact solution of the one- excitation dynamics is provided in terms of…
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.…
We review the subject of perfect state transfer; how one designs the (fixed) interactions of a chain of spins so that a quantum state, initially inserted on one end of the chain, is perfectly transferred to the opposite end in a fixed time.…
Quantum percolation describes the problem of a quantum particle moving through a disordered system. While certain similarities to classical percolation exist, the quantum case has additional complexity due to the possibility of Anderson…
Quantum state transfer is investigated beyond the nearest-neighbour coupling scheme in long spin-$\frac{1}{2}$ linear chains. Exploiting the properties of the next-nearest neighbour Hamiltonian's dispersion relation, it is shown that with…
We consider the state transfer properties of continuous time quantum walks on trees of diameter 4. We characterize all pairs of strongly cospectral vertices in trees of diameter 4, finding that they fall into pairs of three different types.…
Quantum-state transfer with fidelity higher than 0.99 can be achieved in the ballistic regime of an arbitrarily long one-dimensional chain with uniform nearest-neighbor interaction, except for the two pairs of mirror symmetric extremal…
In this article, we consider a spin-spin interaction network governed by $XX + YY$ Hamiltonian. The vertices and edges of the network represent the spin objects and their interactions, respectively. We take a privilege to switch on or off…
A robust quantum state transfer scheme is discussed for three atoms that are trapped by separated cavities linked via optical fibers in ring-connection. It is shown that, under the effective three-atom Ising model, arbitrary quantum state…
This article is devoted to the development of analytical and numerical approaches to the problem of the end-to-end quantum state transfer along the spin-1/2 chain using two methods: (a) a homogeneous spin chain with week end bonds and equal…
Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the…
Quantum walks on graphs are fundamental to quantum computing and have led to many interesting open problems in algebraic graph theory. This review article highlights three key classes of open problems in this domain; perfect state transfer,…
Efficient quantum-state transfer is achieved in a uniformly coupled spin-1/2 chain, with open boundaries, by application of local magnetic fields on the second and last-but-one spins, respectively. These effective \textit{barriers} induce…
Perfect state transfer and fractional revival can be used to move information between pairs of vertices in a quantum network. While perfect state transfer has received a lot of attention, fractional revival is newer and less studied. One…
We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical…
Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and…
We study perfect state transfer on quantum networks represented by weighted graphs. Our focus is on graphs constructed from the join and related graph operators. Some specific results we prove include: (1) The join of a weighted two-vertex…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…