Related papers: Controlling quantum walks with coin eigenstates
This paper discusses continuous-time quantum walks and asymptotic state transfer in graphs with an involution. By providing quantitative bounds on the eigenvectors of the Hamiltonian, it provides an approach to achieving high-fidelity state…
We examine the physical implementation of a discrete time quantum walk with a four-dimensional coin. Our quantum walker is a photon moving repeatedly through a time delay loop, with time being our position space. The quantum coin is…
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…
Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with…
The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. One-dimensional quantum walk…
Measuring a quantum system can randomly perturb its state. The strength and nature of this back-action depends on the quantity which is measured. In a partial measurement performed by an ideal apparatus, quantum physics predicts that the…
In this work we present a model qubit whose basis states are eigenstates of a multi-layered quantum dot. We show that the proper design of the quantum dot results in qubit states that have excellent dynamical properties when a…
We introduce an elementary quantum system consisting of a set of spins on a graph and a particle hopping between its nodes. The quantum state is build sequentially, applying a unitary transformation that couples neighboring spins and, at a…
We study a quantum walker on a one-dimensional lattice with a single defect site characterized by a phase. The spread and localization of discrete-time quantum walks starting at the impurity site are affected by the appearance of bound…
Quantum walk (QW) is the quantum analog of the random walk. QW is an integral part of the development of numerous quantum algorithms. Hence, an in-depth understanding of QW helps us to grasp the quantum algorithms. We revisit the…
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…
We consider a discrete-time 2-state quantum walk on the line. The state of the quantum walker evolves according to a rule which is determined by a coin-flip operator and a position-shift operator. In this paper we take a 3-periodic time…
In this article, we propose a quantum communication protocol via 2-step discrete time quantum walks with two coins on a graph of 10 vertices containing both cycles and paths. Quantum walks are known for their ability to integrate quantum…
We introduce and study a class of discrete-time quantum walks on a one-dimensional lattice. In contrast to the standard homogeneous quantum walks, coin operators are inhomogeneous and depend on their positions in this class of models. The…
We report on a discrete-time quantum walk that uses the momentum of ultra-cold rubidium-87 atoms as the walk space and two internal atomic states as the coin degree of freedom. Each step of the walk consists of a coin toss (a microwave…
Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks…
In this paper, we consider a spectral analysis of discrete time quantum walks on the path. For isospectral coin cases, we show that the time averaged distribution and stationary distributions of the quantum walks are described by the pair…
We study the asymptotic position distribution of general quantum walks on a lattice, including walks with a random coin, which is chosen from step to step by a general Markov chain. In the unitary (i.e., non-random) case, we allow any…
We analyze the asymptotic scaling of persistence of unvisited sites for quantum walks on a line. In contrast to the classical random walk there is no connection between the behaviour of persistence and the scaling of variance. In…
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…