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Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the…
In this paper, the 2-state decomposed-type quantum walk (DQW) on a line is introduced as an extension of the 2-state quantum walk (QW). The time evolution of the DQW is defined with two different matrices, one is assigned to a real…
In the note we show how the choice of the initial states can influence the evolution of time-averaged probability distribution of the quantum walk on even cycles.
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…
In this article we continue the study of the quenched distributions of transient, one-dimensional random walks in a random environment. In a previous article we showed that while the quenched distributions of the hitting times do not…
Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the…
While completely self-avoiding quantum walks have the distinct property of leading to a trivial unidirectional transport of a quantum state, an interesting and non-trivial dynamics can be constructed by restricting the self-avoidance to a…
We employ the broken-link model to create a barrier with slits in a two-dimensional lattice. The diffraction and interference patterns of the probability distribution of quantum walkers passing through the slits are analyzed. Simulations…
We explore a discrete-time, coined quantum walk on a quantum network where the coherent superposition of walker-moves originates from the unitary interaction of the walker-coin with the qubit degrees of freedom in the quantum network. The…
Quantum key distribution is one of the most fundamental cryptographic protocols. Quantum walks are important primitives for computing. In this paper we take advantage of the properties of quantum walks to design new secure quantum key…
We discuss spreading estimates for dynamical systems given by the iteration of an extended CMV matrix. Using a connection due to Cantero--Gr\"unbaum--Moral--Vel\'azquez, this enables us to study spreading rates for quantum walks in one…
In quantum computation theory, quantum random walks have been utilized by many quantum search algorithms which provide improved performance over their classical counterparts. However, due to the importance of the quantum decoherence…
Localization phenomena of quantum walks makes the propagation dynamics of a walker strikingly different from that corresponding to classical random walks. In this paper, we study the localization phenomena of four-state discrete-time…
We analyze the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the…
A quantum central limit theorem for a continuous-time quantum walk on a homogeneous tree is derived from quantum probability theory. As a consequence, a new type of limit theorems for another continuous-time walk introduced by the walk is…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
There has recently been considerable interest in quantum walks in connection with quantum computing. The walk can be considered as a quantum version of the so-called correlated random walk. We clarify a strong structural similarity between…
We analyze two families of three-state quantum walks which show the localization effect. We focus on the role of the initial coin state and its coherence in controlling the properties of the quantum walk. In particular, we show that the…
Absorption of two-state coined quantum walks on a finite line with two sinks located at $N$ and $-N$ is investigated. Elaborating on the results of Konno et al., J. Phys. A: Math. Gen. 36 241 (2003), we derive closed formulas for the…
In this work, we study the effect of a moving detector on a discrete time one dimensional Quantum Random Walk where the movement is realized in the form of hopping/shifts. The occupation probability $f(x,t;n,s)$ is estimated as the number…