Related papers: Stroboscopic quantum walks
Quantum walks are a well-established model for the study of coherent transport phenomena and provide a universal platform in quantum information theory. Dynamically influencing the walker's evolution gives a high degree of flexibility for…
We study the quantum walk in momentum space using a coin arranged in quasi-periodic sequences following a Fibonacci prescription. We build for this system a classical map based on the trace of the evolution operator. The sub-ballistic…
The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks…
A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A new family of $2D$ walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac…
Quantum walks have been shown to be fruitful tools in analysing the dynamic properties of quantum systems. This article proposes to use quantum walks as an approach to Quantum Neural Networks (QNNs). QNNs replace binary McCulloch-Pitts…
Classical random walks and Markov processes are easily described by Hopf algebras. It is also known that groups and Hopf algebras (quantum groups) lead to classical and quantum diffusions. We study here the more primitive notion of a…
We demonstrate a quantum walk with time-dependent coin bias. With this technique we realize an experimental single-photon one-dimensional quantum walk with a linearly-ramped time-dependent coin flip operation and thereby demonstrate two…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
Quantum walks are dynamic systems with a wide range of applications in quantum computation and quantum simulation of analog systems, therefore it is of common interest to understand what changes from an isolated process to one embedded in…
The connection between coined and continuous-time quantum walk models has been addressed in a number of papers. In most of those studies, the continuous-time model is derived from coined quantum walks by employing dimensional reduction and…
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…
We introduce a variation of the discrete time quantum walk, the nonreversal quantum walk, which does not step back onto a position which it has just occupied. This allows us to simulate a dimer and we achieve it by introducing a new type of…
It has been shown classically that combining two chaotic random walks can yield an ordered(periodic) walk. Our aim in this paper is to find a quantum analog for this rather counter-intuitive result. We study chaotic and periodic nature of…
We study a quantum walk of a single particle that is subject to stroboscopic projective measurements on a graph with two sites. This two-level system is the minimal model of a measurement induced quantum walk. The mean first detected…
We unveil a mechanism for generating oscillations with arbitrary multiplets of the period of a given external drive, in long-range interacting quantum many-particle spin systems. These oscillations break discrete time translation symmetry…
Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent…
We study a 2-D disordered time-discrete quantum walk based on 1-D `generalized elephant quantum walk' where an entangling coin operator is assumed and which paves the way to a new set of properties. We show that considering a given disorder…
We propose a scheme for the realization of a quantum walker and a quantum simulator for the Dirac equation with ultracold spinor atoms in driven optical lattices. A precise control of the dynamics of the atomic matter wave can be realized…
We put forward a new, versatile and highly-scalable experimental setup for the realization of discrete two-dimensional quantum random walks with a single-qubit coin and tunable degree of decoherence. The proposed scheme makes use of a small…
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…