Related papers: Geodesic Quantum Walks
We treat a quantum walk (QW) on the line whose quantum coin at each vertex tends to be the identity as the distance goes to infinity. We obtain a limit theorem that this QW exhibits localization with not an exponential but a "power-law"…
Continuous-time quantum walks (CTQWs) provide a valuable model for quantum transport, universal quantum computation and quantum spatial search, among others. Recently, the empowering role of new degrees of freedom in the Hamiltonian…
Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…
We present a comprehensive classification of one-dimensional coined quantum walks on the infinite line, focusing on the spatial probability distributions they induce. Building on prior results, we identify all initial coin states that lead…
Based on studies on four specific networks, we conjecture a general relation between the walk dimensions $d_{w}$ of discrete-time random walks and quantum walks with the (self-inverse) Grover coin. In each case, we find that $d_{w}$ of the…
In this paper, we introduce a discrete quantum walk model called bipartite walks. Bipartite walks include many known discrete quantum walk models, like arc-reversal walks, vertex-face walks. For the transition matrix of a quantum walk,…
The weak convergence theorems of the one- and two-dimensional simple quantum walks, SQW$^{(d)}, d=1,2$, show a striking contrast to the classical counterparts, the simple random walks, SRW$^{(d)}$. The limit distributions have novel…
Inspired by the classical phenomenon of random walk, the concept of quantum walk has emerged recently as a powerful platform for the dynamical simulation of complex quantum systems, entanglement production and universal quantum computation.…
In this paper we consider quantum walks whose evolution converges to the Dirac equation one in the limit of small wave-vectors. We show exact Fast Fourier implementation of the Dirac quantum walks in one, two and three space dimensions. The…
By pursuing the deep relation between the one-dimensional Dirac equation and quantum walks, the physical role of quantum interference in the latter is explained. It is shown that the time evolution of the probability density of a quantum…
We study a 2-D disordered time-discrete quantum walk based on 1-D `generalized elephant quantum walk' where an entangling coin operator is assumed and which paves the way to a new set of properties. We show that considering a given disorder…
We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…
Quantum walks represent paradigmatic quantum evolutions, enabling powerful applications in the context of topological physics and quantum computation. They have been implemented in diverse photonic architectures, but the realization of a…
Quantum walks are recognizably useful for the development of new quantum algorithms, as well as for the investigation of several physical phenomena in quantum systems. Actual implementations of quantum walks face technological difficulties…
We prove analytical results showing that decoherence can be useful for mixing time in a continuous-time quantum walk on finite cycles. This complements the numerical observations by Kendon and Tregenna (Physical Review A 67 (2003), 042315)…
We study the distributions of the continuous-time quantum walk on a one-dimensional lattice. In particular we will consider walks on unbounded lattices, walks with one and two boundaries and Dirichlet boundary conditions, and walks with…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
Discrete-time quantum walk in one-dimension is studied from a path-integral perspective. This enables derivation of a closed-form expression for amplitudes corresponding to any coin-position basis of the state vector of the quantum walker…
The discrete time quantum walk which is a quantum counterpart of random walk plays important roles in the theory of quantum information theory. In the present paper, we focus on discrete time quantum walks viewed as quantization of random…
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…