Related papers: Design for implementation of discrete-time quantum…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…
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…
Recently, the quaternionic quantum walk was formulated by the first author as a generalization of discrete-time quantum walks. We treat the right eigenvalue problem of quaternionic matrices to analysis the spectra of its transition matrix.…
It was recently shown that continuous-time quantum walks on dynamic graphs, i.e., sequences of static graphs whose edges change at specific times, can implement a universal set of quantum gates. This result treated all isolated vertices as…
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…
We consider a Grover walk model on a finite internal graph, which is connected with a finite number of semi-infinite length paths and receives the alternative inflows along these paths at each time step. After the long time scale, we know…
Advances in recent years have made it possible to explore quantum dots as a viable technology for scalable quantum information processing. Charge qubits for example can be realized in the lowest bound states of coupled quantum dots and the…
Quantum random walks are shown to have non-intuitive dynamics, which makes them an attractive area of study for devising quantum algorithms for well-known classical problems as well as those arising in the field of quantum computing. In…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
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 introduce the driven discrete time quantum walk, where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original quantum…
We extend the idea of a discrete-time quantum walk on a graph by placing a qubit on each vertex, and allowing the walker to interact with the qubit at its current position. We show that allowing for a controlled-Z interaction at each time…
Discrete-time quantum walk in one-dimension is studied from a path-integral perspective. This enables derivation of a closed-form expression for amplitudes corresponding to any coin-position basis of the state vector of the quantum walker…
The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range…
The quantum random walk has drawn special interests because its remarkable features to the classical counterpart could lead to new quantum algorithms. In this paper, we propose a feasible scheme to implement quantum random walks on a line…
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…
The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with $n$ wires, each corresponding to one…
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…
We investigate the counterparts of random walk in universal quantum computing and their implementation using standard quantum circuits. Quantum walk have been recently well investigated for traversing graphs with certain oracles. We focus…