Related papers: Intertwining operators between one-dimensional hom…
Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
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…
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…
Multilayer network is a potent platform which paves a way to study the interactions among entities in various networks with multiple types of relationships. In this study, the dynamics of discrete-time quantum walk on a multilayer network…
Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In…
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an…
Quantum walks provide a framework for understanding and designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a…
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…
Quantum walks have wide applications in quantum information, such as universal quantum computation, so it is important to explore properties of quantum walks thoroughly. We propose a novel method to implement discrete-time quantum walks…
Mathematical analysis of the spectral properties of the time evolution operator in quantum walks is essential for understanding key dynamical behaviors such as localization and long-term evolution. The inhomogeneous three-state case, in…
We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…
Quantum walks are the quantum mechanical analogue of classical random walks and an extremely powerful tool in quantum simulations, quantum search algorithms, and even for universal quantum computing. In our work, we have designed and…
The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between…
Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal.…
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-…
Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There are two types of quantum walks. One is the discrete-time…
Quantum walks are known to propagate quadratically faster than their classical counterparts and are used to model dynamics in various quantum systems. The spread of the quantum walk in position space shows anomalous diffusion behavior. By…
This study investigated the unitary equivalent classes of one-dimensional quantum walks. We determined the unitary equivalent classes of one-dimensional quantum walks, two-phase quantum walks with one defect, complete two-phase quantum…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…