In this paper we study a one-dimensional quantum random walk with the Hadamard transformation which is often called the Hadamard walk. We construct the Hadamard walk using a transition matrix on probability amplitude and give some results on symmetricity of probability distributions for the Hadamard walk.

In this paper we extend the concept of persistence, well defined for classical stochastic dynamics, to the context of quantum dynamics. We demonstrate the idea via quantum random walk and a successive measurement scheme, where persistence is defined as the time during which a given site remains unvisited by the walker. We also investigated the behavior of related quantities, e.g., the first-pas...

Shenvi, Kempe and Whaley’s quantum random-walk search (SKW) algorithm [2003 Phys. Rev. A 67 052307] is known to require O( √ N) number of oracle queries to find the marked element, where N is the size of the search space. This scaling is thought to be the best achievable on a quantum computer. We prove that the final state of the quantum walk in the SKW algorithm yields the nearest neighbours o...

It is shown in this paper that the quantum master equation can be mapped to a modified continuous time random walk (CTRW) if the relaxation term is composed of transitions over a set of states. When the Hamiltonian is time-independent and transitions are between its eigenlevels, such a modified CTRW reduces to the Markovian walk equivalent to the Pauli master equation. On the other hand, the me...

One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we “quantize” the classical random walk by finding, subject to a certain condition of “strong positivity”, the most general Markovian, translationally invariant “decoherence functional” with nearest neighbor transitions.

Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel properties to gain an algorithmic speed-up over classical algorithms. In this paper, we present a quantum search algorithm based on the quantum random walk architectu...

We consider crossovers with respect to the weak convergence theorems from a discretetime quantum walk (DTQW). We show that a continuous-time quantum walk (CTQW) and discreteand continuous-time random walks can be expressed as DTQWs in some limits. At first we generalize our previous study [Phys. Rev. A 81, 062129 (2010)] on the DTQW with position measurements. We show that the position measurem...

We generalize the quantum random walk (QRW) protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave function evolutions. Quasiperiodic sequences, following the Fibonacci prescription, are of particular interest, leading to a sub-ballistic wavefunction spreading....