Related papers: Quantization and Asymptotic Behaviour of $\epsilon…
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 discuss the model of a one-dimensional, discrete-time walk on a line with spatial heterogeneity in the form of a variable set of ultrametric barriers. Inspired by the homogeneous quantum walk on a line, we develop a formalism by which…
Quantum walks are promising for information processing tasks because on regular graphs they spread quadratically faster than random walks. Static disorder, however, can turn the tables: unlike random walks, quantum walks can suffer Anderson…
We consider a two-state quantum walk on a line where after the first step an absorbing sink is placed at the origin. The probability of finding the walker at position $j$, conditioned on that it has not returned to the origin, is…
It is well known that many real world networks have the power-law degree distribution (scale-free property). However there are no rigorous results for continuous-time quantum walks on such realistic graphs. In this paper, we analyze…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
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…
This paper continues the study of large time behavior of a nonlinear quantum walk begun in arXiv:1801.03214. In this paper, we provide a weak limit theorem for the distribution of the nonlinear quantum walk. The proof is based on the…
We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a…
The coin-position entanglement generated by the evolution operator of a discrete--time quantum walk converges, in the long time limit, to a well defined value which depends on the initial state. We also discuss the asymptotic bi-partite…
In quantum computation theory, quantum random walks have been utilized by many quantum search algorithms which provide improved performance over their classical counterparts. However, due to the importance of the quantum decoherence…
The quantum walk (QW) is the term given to a family of algorithms governing the evolution of a discrete quantum system and as such has a founding role in the study of quantum computation. We contribute to the investigation of QW phenomena…
Quantum walks are known to have nontrivial interactions with absorbing boundaries. In particular it has been shown that an absorbing boundary in the one dimensional quantum walk partially reflects information, as observed by absorption…
A classical lazy random walk on cycles is known to mix to the uniform distribution. In contrast, we show that a continuous-time quantum walk on cycles exhibit strong non-uniform mixing properties. Our results include the following: - The…
We show that the coined quantum walk on a line can be understood as an interference phenomenon, can be classically implemented, and indeed already has been. The walk is essentially two independent walks associated with the different coin…
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…
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
We demonstrate an alternative method for calculating the asymptotic behaviour of the discrete one-coin quantum walk on the infinite line, via the Jacobi polynomials that arise in the path integral representation. This is significantly…
We investigate a space-inhomogeneous discrete-time quantum walk in one dimension. We show that the walk exhibits localization by a path counting method.
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…