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A Plastic Quantum Walk admits both continuous time and continuous spacetime. The model has been recently proposed by one of the authors in \cite{molfetta2019quantum}, leading to a general quantum simulation scheme for simulating fermions in…
We study the absorption time and spreading rate of the discrete-time quantum walk propagating on a line in the presence or absence of an absorber. We analytically establish that in the presence of an absorber, the average absorption time of…
We present a detailed analysis of continuous time quantum walks (CTQW) with both position and transition defects defined at a single point in the line. Analytical solutions of both traveling waves or bound states are obtained, which provide…
We propose a new multi-dimensional discrete-time quantum walk (DTQW), whose continuum limit is an extended multi-dimensional Dirac equation, which can be further mapped to the Schr\"{o}dinger equation. We show in two ways that our DTQW is…
In this Chapter, we present some interesting properties of quantum walks on the line. We concentrate our attention in the emergence of invariance and provide some insights into the ultimate origin of the observed behavior. In the first part…
We consider a new model of quantum walk on a one-dimensional momentum space that includes both discrete jumps and continuous drift. Its time evolution has two stages; a Markov diffusion followed by localized dynamics. As in the well known…
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…
The formalism of continuous-time quantum walks on graphs has been widely used in the study of quantum transport of energy and information, as well as in the development of quantum algorithms. In experimental settings, however, there is…
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…
Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. To be analogous to the hitting time for a classical walk, the quantum hitting time must involve repeated measurements as…
The n-dimensional hypercube quantum random walk (QRW) is a particularily appealing example of a quantum walk because it has a natural implementation on a register on $n$ qubits. However, any real implementation will encounter decoherence…
We present a quantum-dynamical framework for identifying structurally important residues in proteins based on continuous time quantum walks (CTQWs) on weighted residue interaction networks constructed from experimentally resolved…
Recent findings suggest that processes such as the electronic energy transfer through the photosynthetic antenna display quantal features, aspects known from the dynamics of charge carriers along polymer backbones. Hence, in modeling energy…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
Open Quantum Walks (OQWs), originally introduced by S. Attal, are quantum generalizations of classical Markov chains. Recently, natural continuous time models of OQW have been developed by C. Pellegrini. These models, called Continuous Time…
We generalize the discrete quantum walk on the line using a time dependent unitary coin operator. We find an analytical relation between the long-time behaviors of the standard deviation and the coin operator. Selecting the coin time…
Rules for quantizing the walker+coin parts of a classical random walk are provided by treating them as interacting quantum systems. A quantum optical random walk (QORW), is introduced by means of a new rule that treats quantum or classical…
In discrete time, coined quantum walks, the coin degrees of freedom offer the potential for a wider range of controls over the evolution of the walk than are available in the continuous time quantum walk. This paper explores some of the…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
Periodically-driven quantum systems can exhibit topologically non-trivial behaviour, even when their quasi-energy bands have zero Chern numbers. Much work has been conducted on non-interacting quantum-mechanical models where this kind of…