Related papers: Two-particle scattering on general graphs
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…
Quantum walks have been used to develop quantum algorithms since their inception, and can be seen as an alternative to the usual circuit model; combining single-particle quantum walks on sparse graphs with two-particle scattering on a line…
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…
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…
We consider the effects of plane-wave states scattering off finite graphs, as an approach to implementing single-qubit unitary operations within the continuous-time quantum walk framework of universal quantum computation. Four semi-infinite…
We study scattering quantum walks on highly symmetric graphs and use the walks to solve search problems on these graphs. The particle making the walk resides on the edges of the graph, and at each time step scatters at the vertices. All of…
We set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible.…
We show how to construct discrete-time quantum walks on directed, Eulerian graphs. These graphs have tails on which the particle making the walk propagates freely, and this makes it possible to analyze the walks in terms of scattering…
A quantum walk model which reflects the $2$-cell embedding on the orientable closed surface of a graph in the dynamics is introduced. We show that the scattering matrix is obtained by finding the faces on the underlying surface which have…
Quantum walks are roughly analogous to classical random walks, and like classical walks they have been used to find new (quantum) algorithms. When studying the behavior of large graphs or combinations of graphs it is useful to find the…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
Quantum walks have frequently envisioned the behavior of a quantum state traversing a classically defined, generally finite, graph structure. While this approach has already generated significant results, it imposes a strong assumption: all…
Certain continuous-time quantum walks can be viewed as scattering processes. These processes can perform quantum computations, but it is challenging to design graphs with desired scattering behavior. In this paper, we study and construct…
Quantum graphs can be extended to scattering systems when they are connected by leads to infinity. It is shown that for certain extensions, the scattering matrices of isospectral graphs are conjugate to each other and their poles…
We study scattering of particles which obey an $SU(N)$ global symmetry through the lens of quantum computation and quantum algorithms. We show that for scattering between particles which transform in the fundamental or anti-fundamental…
A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we…
We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…