Related papers: Formal languages analysed by quantum walks
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
Quantum walks are expected to serve important modelling and algorithmic applications in many areas of science and mathematics. Although quantum walks have been successfully implemented physically in recent times, no major efforts have been…
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 quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
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…
In this work, we introduce a general form of a two-parameter family of local interactions between quantum walkers conditioned on the internal state of their coins. By choosing their particular case, we systematically study the impact of…
In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo momentum space. For some…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
Discrete time quantum walks (DTQWs) are nontrivial generalizations of random walks with a broad scope of applications. In particular, they can be used as computational primitives, and they are suitable tools for simulating other quantum…
The development of universal quantum computers has achieved remarkable success in recent years, culminating with the quantum supremacy reported by Google. Now is possible to implement short-depth quantum circuits with dozens of qubits and…
Continuous-time quantum walk is one of the alternative approaches to quantum computation, where a universal set of quantum gates can be achieved by scattering a quantum walker on some specially-designed structures embedded in a sparse graph…
This manuscript gathers and subsumes a long series of works on using QW to simulate transport phenomena. Quantum Walks (QWs) consist of single and isolated quantum systems, evolving in discrete or continuous time steps according to a…
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…
The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, led rapidly to several new quantum algorithms. These all follow unitary quantum evolution, apart from the final…
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…
The two major discrete time formulations for quantum walks, coined and scattering, are unitarily equivalent for arbitrary position dependent transition amplitudes and any topology (PRA {\bf 80}, 052301 (2009)). Although the proof explicit…
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.…
We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way,…
Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…
We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.