Related papers: Two-state quantum walk on two- and three-dimension…
From the unitary operator used for implementing two-state discrete-time quantum walk on one-, two- and three- dimensional lattice we obtain a two-component Dirac-like Hamiltonian. In particular, using different pairs of Pauli basis as…
Multi-dimensional quantum walks usually require large coin spaces. Here we show that the non-localized case of the spatial density probability of the two-dimensional Grover walk can be obtained using only a two-dimensional coin space and a…
We analyze the role of dimensionality in the time evolution of discrete time quantum walks through the example of the three-state walk on a two-dimensional, triangular lattice. We show that the three-state Grover walk does not lead to…
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 have recently proposed a two-dimensional quantum walk where the requirement of a higher dimensionality of the coin space is substituted with the alternance of the directions in which the walker can move [C. Di Franco, M. Mc Gettrick, and…
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…
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…
Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…
High-dimensional quantum systems can offer extended possibilities and multiple advantages while developing advanced quantum technologies. In this paper, we propose a class of quantum-walk architecture networks that admit the efficient…
Exploiting multi-dimensional quantum walks as feasible platforms for quantum computation and quantum simulation is attracting constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional…
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…
The quantum walk is a quantum counterpart of the classical random walk that exhibits nonclassical behaviors and outperforms the classical random walk in various aspects. It has been known that a single particle can be propagated by a…
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…
We introduce and analyze a one-dimensional quantum walk with two time-independent rotations on the coin. We study the influence on the property of quantum walk due to the second rotation on the coin. Based on the asymptotic solution in the…
We propose a novel implementation of discrete time quantum walks for a neutral atom in an array of optical microtraps or an optical lattice. We analyze a one-dimensional walk in position space, with the coin, the additional qubit degree of…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…
We implement the discrete-time quantum walk model using the continuous-time evolution of the Hamiltonian that includes both the shift and the coin generators. Based on the Trotter-Suzuki first-order approximation, we consider an…
In this article, we undertake a detailed study of the limiting behavior of a three-state discrete-time quantum walk on one dimensional lattice with generalized Grover coins. Two limit theorems are proved and consequently we show that the…
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…