Related papers: Quantum walk of a trapped ion in phase space
The behaviors of one-dimensional quantum random walks are strikingly different from those of classical ones. However, when decoherence is involved, the limiting distributions take on many classical features over time. In this paper, we…
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…
We propose a scheme of quantum error correction that employs a multi-particle quantum walk defined on nested squares, each hosting a single particle. In this model, each particle moves within its own distinct square through iterations of…
Quantum coherence is one of the clearest departures from classical physics, exhibited when a system is in a superposition of different basis states. Here the coherent superposition of three motional Fock states of a single trapped ion is…
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…
This study investigate the unitary equivalence classes of quantum walks on cycles. We show that unitary equivalence classes of quantum walks on a cycle with $N$ vertices are parameterized by $2N$ real parameters. Moreover, the ranges of two…
Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which…
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…
Classical random walk formalism shows a significant role across a wide range of applications. As its quantum counterpart, the quantum walk is proposed as an important theoretical model for quantum computing. By exploiting the quantum…
Quantum walks are considered in a one-dimensional random medium characterized by static or dynamic disorder. Quantum interference for static disorder can lead to Anderson localization which completely hinders the quantum walk and it is…
We provide an algorithm that factorizes one-dimensional quantum walks into a protocol of two basic operations: A fixed conditional shift that transports particles between cells and suitable coin operators that act locally in each cell. This…
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…
Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example…
We realize quasi-periodic dynamics of a quantum walker over 2.5 quasi-periods by realizing the walker as a single photon passing through a quantum-walk optical-interferometer network. We introduce fully controllable polarization-independent…
In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in…
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…
We present an efficient general method for realizing a quantum walk operator corresponding to an arbitrary sparse classical random walk. Our approach is based on Grover and Rudolph's method for preparing coherent versions of efficiently…
Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I…
We consider asymptotic behaviour of a Hadamard walk on a cycle. For a walk which starts with a state in which all the probability is concentrated on one node, we find the explicit formula for the limiting distribution and discuss its…
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…