Related papers: Perfect State Transfer on Oriented Graphs
We study a class of Unitary Quantum Walks on arbitrary graphs, parameterized by a family of scattering matrices. These Scattering Quantum Walks model the discrete dynamics of a system on the edges of the graph, with a scattering process at…
In the light of recent advances in fabricating single layer quantum chips and a possible road toward development of multi-layer quantum chips, we review, in a detailed way, the subject of quantum state transfer with particular emphasis on…
Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…
In this paper, we study the existence of perfect state transfer and pretty good state transfer in vertex complemented coronas. We prove that perfect state transfer in vertex complemented coronas is extremely rare. In contrast, we give…
We introduce some new perfect state transfer and teleportation schemes by quantum walks with two coins. Encoding the transferred information in coin 1 state and alternatively using two coin operators, we can perfectly recover the…
We introduce a model of a quantum walk on a graph in which a particle jumps between neighboring nodes and interacts with independent spins sitting on the edges. Entanglement propagates with the walker. We apply this model to the case of a…
For a given hypergraph, an orientation can be assigned to the vertex-edge incidences. This orientation is used to define the adjacency and Laplacian matrices. In addition to studying these matrices, several related structures are…
We investigate state transfer on a hypercube by means of a quantum walk where the sender and the receiver vertices are marked by a weighted loops. First, we analyze search for a single marked vertex, which can be used for state transfer…
We have generalised the concept of graph states to what we have called mixed graph states, which we define in terms of mixed graphs, that is graphs with both directed and undirected edges, as the density matrix stabilized by the associated…
We propose a protocol for perfect state transfer between any pair of vertices in a hypercube. Given a pair of distinct vertices in the hypercube we determine a sub-hypercube that contains the pair of vertices as antipodal vertices. Then a…
High-dimensional quantum systems can offer extended possibilities and multiple advantages while developing advanced quantum technologies. In this paper, we propose a class of quantum-walk architecture networks that admit the efficient…
In light of recent interest in Hadamard diagonalisable graphs (graphs whose Laplacian matrix is diagonalisable by a Hadamard matrix), we generalise this notion from real to complex Hadamard matrices. We give some basic properties and…
I introduce a new type of continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First I analyze the quantum snake walk on the line, and I…
Probabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure…
We introduce a scheme for perfect state transfer in regular two and three dimensional structures. The interactions on the lattices are of XX spin type with uniform couplings. In two dimensions the structure is a hexagonal lattice and in…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
In this paper, we introduce random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension $d$, a random walk with an absorbing state is defined which relates to the spectrum of the $k$-dimensional…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…
We propose a family of lagged random walk sampling methods in simple undirected graphs, where transition to the next state (i.e. node) depends on both the current and previous states -- hence, lagged. The existing random walk sampling…