Related papers: Implementation of Continuous-Time Quantum Walk on …
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
In some of the earliest work on quantum mechanical computers, Feynman showed how to implement universal quantum computation by the dynamics of a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is…
The finite dihedral group generated by one rotation and one reflection 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…
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…
The connection between coined and continuous-time quantum walk models has been addressed in a number of papers. In most of those studies, the continuous-time model is derived from coined quantum walks by employing dimensional reduction and…
Quantum walks, both discrete (coined) and continuous time, form the basis of several recent quantum algorithms. Here we use numerical simulations to study the properties of discrete, coined quantum walks. We investigate the variation in the…
Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…
Non-local higher-energy auxiliary states have been successfully used to entangle pairs of qubits in different quantum computing systems. Typically a longer-span non-local state or sequential application of few-qubit entangling gates are…
In this paper, we show reduction methods for search algorithms on graphs using quantum walks. By using a graph partitioning method called equitable partition for the the given graph, we determine "effective subspace" for the search…
Testing graph completeness is a critical problem in computer science and network theory. Leveraging quantum computation, we present an efficient algorithm using the Szegedy quantum walk and quantum phase estimation (QPE). Our algorithm,…
Quantum walks, being the quantum analogue of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the `glued trees' algorithm, which provides…
Quantum magnetometry uses quantum resources to measure magnetic fields with precision and accuracy that cannot be achieved by its classical counterparts. In this paper, we propose a scheme for quantum magnetometry using discrete-time…
In recent years, quantum walks have been widely researched and have shown exciting properties. One such is a quadratic speed-up in hitting time compared to its classical counterpart. In this paper, we design a quantum circuit for the MNRS…
Quantum walks are recognizably useful for the development of new quantum algorithms, as well as for the investigation of several physical phenomena in quantum systems. Actual implementations of quantum walks face technological difficulties…
We study how quantum walks can be used to find structural anomalies in graphs via several examples. Two of our examples are based on star graphs, graphs with a single central vertex to which the other vertices, which we call external…
In this paper we study discrete-time quantum walks on Cayley graphs corresponding to Dihedral groups, which are graphs with both directed and undirected edges. We consider the walks with coins that are one-parameter continuous deformation…
In this paper, we study decoherence in continuous-time quantum walks (CTQWs) on one-dimension regular networks. For this purpose, we assume that every node is represented by a quantum dot continuously monitored by an individual point…
Discrete-time quantum walks (DTQWs) provide a convenient platform for a realisation of many topological phases in noninteracting systems. They often offer more possibilities than systems with a static Hamiltonian. Nevertheless, researchers…
In this paper we show how using complex valued edge weights in a graph can completely suppress the flow of probability amplitude in a continuous time quantum walk to specific vertices of the graph when the edge weights, graph topology and…
We address continuous-time quantum walks on graphs in the presence of time- and space-dependent noise. Noise is modeled as generalized dynamical percolation, i.e. classical time-dependent fluctuations affecting the tunneling amplitudes of…