Related papers: Quantum state revivals in quantum walks on cycles
We report on the possibility of controlling quantum random walks with a step-dependent coin. The coin is characterized by a (single) rotation angle. Considering different rotation angles, one can find diverse probability distributions for…
We set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible.…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
Random walks are fundamental models of stochastic processes with applications in various fields including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on…
We consider recurrence to the initial state after repeated actions of a quantum channel. After each iteration a projective measurement is applied to check recurrence. The corresponding return time is known to be an integer for the special…
A quantum walker moves on the integers with four extra degrees of freedom, performing a coin-shift operation to alter its internal state and position at discrete units of time. The time evolution is described by a unitary process. We focus…
In this paper we develop the topics of Quantum Recurrences and of Quantum Fidelity which have attracted great interest in recent years. The return probability is given by the square modulus of the overlap between a given initial wavepacket…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
We introduce the quantum quincunx, which physically demonstrates the quantum walk and is analogous to Galton's quincunx for demonstrating the random walk. In contradistinction to the theoretical studies of quantum walks over orthogonal…
The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially…
We study a quantum walk in one-dimension using two different "coin" operators. By mixing two operators, both of which give a biased walk with negative expectation value for the walker position, it is possible to reverse the bias through…
Quantum Stochastic Walks (QSW) allow for a generalization of both quantum and classical random walks by describing the dynamic evolution of an open quantum system on a network, with nodes corresponding to quantum states of a fixed basis. We…
For a discrete time quantum walk (QW) on the $N$-cycle, allowing for decoherence on the coin, we derive a number of new results, including an explicit formula for the position probability distribution. For a QW of this type, we show that…
Recently Mc Gettrick [1] introduced and studied a discrete-time 2-state quantum walk (QW) with a memory in one dimension. He gave an expression for the amplitude of the QW by path counting method. Moreover he showed that the return…
Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is observed at a location with a probability. The finding…
The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…
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…