Related papers: Discrete-time quantum walk with feed-forward quant…
The Dirac equation can be modelled as a quantum walk, with the quantum walk being: discrete in time and space (i.e. a unitary evolution of the wave-function of a particle on a lattice); homogeneous (i.e. translation-invariant and…
A quantum computer, i.e. utilizing the resources of quantum physics, superposition of states and entanglement, could furnish an exponential gain in computing time. A simulation using such resources is called a quantum simulation. The…
In this letter we introduce the concept of a driven quantum walk. This work is motivated by recent theoretical and experimental progress that combines quantum walks and parametric down- conversion, leading to fundamentally different…
We look at two possible routes to classical behavior for the discrete quantum random walk on the line: decoherence in the quantum ``coin'' which drives the walk, or the use of higher-dimensional coins to dilute the effects of interference.…
The properties of the coinless quantum walk model have not been as thoroughly analyzed as those of the coined model. Both evolve in discrete time steps but the former uses a smaller Hilbert space, which is spanned merely by the site basis.…
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…
We consider a discrete-time 2-state quantum walk on the line. The state of the quantum walker evolves according to a rule which is determined by a coin-flip operator and a position-shift operator. In this paper we take a 3-periodic time…
The analysis of logarithmic return distributions defined over large time scales is crucial for understanding the long-term dynamics of asset price movements. For large time scales of the order of two trading years, the anticipated Gaussian…
We introduce an analytically treatable spin decoherence model for quantum walk on a line that yields the exact position probability distribution of an unbiased classical random walk at all-time scales. This spin decoherence model depicts a…
Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal…
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the…
Efficient simulations of the dynamics of open systems is of wide importance for quantum science and tech-nology. Here, we introduce a generalization of the transfer-tensor, or discrete-time memory kernel, formalism to multi-time measurement…
The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with $n$ wires, each corresponding to one…
The finite dihedral group generated by one rotation and one flip is the simplest case of the non-abelian group. Cayley graphs are diagrammatic counterparts of groups. In this paper, much attention is given to the Cayley graph of the…
We present a novel Adaptive Distribution Generator that leverages a quantum walks-based approach to generate high precision and efficiency of target probability distributions. Our method integrates variational quantum circuits with…
Continuous-time random walks offer powerful coarse-grained descriptions of transport processes. We here microscopically derive such a model for a Brownian particle diffusing in a deep periodic potential. We determine both the waiting-time…
It has been discovered that open quantum walks diffusively distribute in space, since they were introduced in 2012. Indeed, some limit distributions have been demonstrated and most of them are described by Gaussian distributions. We operate…
One can think of some physical evolutions as being the emergent-effective result of a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide a simple procedure to coarse-grain color-blind quantum cellular…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…