Related papers: Driven Discrete Time Quantum Walks
In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the…
The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain…
Photonics provide an efficient way to implement quantum walks, the quantum analogue of classical random walk that demonstrates rich physics with potential applications. However, most photonic quantum walks do not involve photon…
We present a review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains, based on spatial- and time-multiplexing techniques, respectively. Additionally, we propose a detailed novel scheme…
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…
In this paper, we propose a circuit design for implementing quantum walks on complex networks. Quantum walks are powerful tools for various graph-based applications such as spatial search, community detection, and node classification.…
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…
In discrete time, coined quantum walks, the coin degrees of freedom offer the potential for a wider range of controls over the evolution of the walk than are available in the continuous time quantum walk. This paper explores some of the…
Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There are two types of quantum walks. One is the discrete-time…
We study the absorption time and spreading rate of the discrete-time quantum walk propagating on a line in the presence or absence of an absorber. We analytically establish that in the presence of an absorber, the average absorption time of…
We present an Ito's formula for the one-dimensional discrete-time quantum walk and give some examples including a Tanaka's formula by using the formula. Moreover we discuss integrals for the quantum walk.
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…
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…
Multilayer network is a potent platform which paves a way to study the interactions among entities in various networks with multiple types of relationships. In this study, the dynamics of discrete-time quantum walk on a multilayer network…
We present a discrete-time, one-dimensional quantum walk based on the entanglement between the momentum of ultracold rubidium atoms (the walk space) and two internal atomic states (the "coin" degree of freedom). Our scheme is highly…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. For a long time, these models have interested the community for their nice properties such as locality or translation invariance. This…
A discrete-time Quantum Walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). In this paper, we study the…
The probability distributions of discrete-time quantum walks have been often investigated, and many interesting properties of them have been discovered. The probability that the walker can be find at a position is defined by diagonal…
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…
The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks…