Related papers: Quantum Walk in Momentum Space with a Bose-Einstei…
We propose an implementation of a quantum walk on a circle on an optomechanical system by encoding the walker on the phase space of a radiation field and the coin on a two-level state of a mechanical resonator. The dynamics of the system is…
We propose an implementation scheme for the continuous-time quantum walk using a diatomic molecule and an optical frequency comb. We show an analogy between the quantum walk and the cascade rotational transitions induced by the optical…
In this letter we introduce the concept of a driven quantum walk. This work is motivated by recent theoretical and experimental progress that combines quantum walks and parametric down- conversion, leading to fundamentally different…
The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between…
We analyze the quantum walk on a cycle using discrete Wigner functions as a way to represent the states and the evolution of the walker. The method provides some insight on the nature of the interference effects that make quantum and…
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 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…
One approach to the development of quantum search algorithms is the quantum walk. A spatial search can be effected by the continuous-time evolution of a single quantum particle on a graph containing a marked site. In many physical…
Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable…
The development of universal quantum computers has achieved remarkable success in recent years, culminating with the quantum supremacy reported by Google. Now is possible to implement short-depth quantum circuits with dozens of qubits and…
The quantum walk (QW) has proven to be a valuable testbed for fundamental inquiries in quantum technology applications such as quantum simulation and quantum search algorithms. Many benefits have been found by exploring implementations of…
We introduce the Peierls substitution to a two-dimensional discrete-time quantum walk on a square lattice to examine the spreading dynamics and the coin-position entanglement in the presence of an artificial gauge field. We use the ratio of…
We characterize quantumness of the so-called quantum walks (whose dynamics is governed by quantum mechanics) by introducing two computable measures which are stronger than the variance of the walker's position probability distribution. The…
We simulate various topological phenomena in condense matter, such as formation of different topological phases, boundary and edge states, through two types of quantum walk with step-dependent coins. Particularly, we show that…
We address the performance of a coin-biased quantum walk as a generator for non-classical position states of the walker. We exploit a phenomenon of coherent localisation in the position space --- resulting from the choice of small values of…
This letter treats the quantum random walk on the line determined by a 2 times 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The…
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…
Decoherence transforms a ballistic quantum walk into a diffusive classical random walk. After each step the environment measures the particle's path and the outside world gets to know the which-way information. The relation between the…
A proposal for the implementation of quantum walks using cold atom technology is presented. It consists of one atom trapped in time varying optical superlattices. The required elements are presented in detail including the preparation…
We present a scheme for multi-bit quantum random number generation using a single qubit discrete-time quantum walk in one-dimensional space. Irrespective of the initial state of the qubit, quantum interference and entanglement of particle…