Related papers: Quantum walks in higher dimensions

The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. One-dimensional quantum walk…

This work focuses on the study of quantum stochastic walks, which are a generalization of coherent, i. e. unitary quantum walks. Our main goal is to present a measure of a coherence of the walk. To this end, we utilize the asymptotic…

Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random…

Nowadays, quantum simulation schemes come in two flavours. Either they are continuous-time discrete-space models (a.k.a Hamiltonian-based), pertaining to non-relativistic quantum mechanics. Or they are discrete-spacetime models (a.k.a…

We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…

We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…

We implement the proof of principle for the quantum walk of one ion in a linear ion trap. With a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to its…

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…

A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the…

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…

We investigate the quantum versions of a one-dimensional random walk, whose corresponding Markov Chain is of order 2. This corresponds to the walk having a memory of up to two previous steps. We derive the amplitudes and probabilities for…

Classical optics can be used to efficiently implement certain quantum information processing tasks with a high degree of control, for example, one-dimensional quantum walks through the space of orbital angular momentum of light directed by…

Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…

We study one-dimensional quantum walk with four internal degrees of freedom resulted from two entangled qubits. We will demonstrate that the entanglement between the qubits and its corresponding coin operator enable one to steer the…

This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational…

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…

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…

We introduce a multi-coin discrete quantum random walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying…

Recently, what appears to be a fundamental limit associated with the size of an object that separates the quantum behavior characterizing small objects from the classical behavior characterizing large objects has been derived from the…

We investigate continuous-time quantum walks of two indistinguishable particles (bosons, fermions or hard-core bosons) in one-dimensional lattices with nearest-neighbour interactions. The two interacting particles can undergo independent-…