Related papers: Quantum Search on Simplicial Complexes
In this work, we show that the usage of a quantum gate that gives extra information about the solution searched permits to improve the performance of the search algorithm by switching from quantum to classical search in the appropriated…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
A randomly walking quantum particle searches in Grover's $\Theta(\sqrt{N})$ iterations for a marked vertex on the complete graph of $N$ vertices by repeatedly querying an oracle that flips the amplitude at the marked vertex, scattering by a…
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
Quantum transport across discrete structures is a relevant topic of solid state physics and quantum information science, which can be suitably studied in the context of continuous-time quantum walks. The addition of phases degrees of…
When classically searching a database, having additional correct answers makes the search easier. For a discrete-time quantum walk searching a graph for a marked vertex, however, additional marked vertices can make the search harder by…
One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…
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…
A single excitation in a quantum spin network described by the Heisenberg model can effect a variety of continuous-time quantum walks on unweighted graphs, including those governed by the discrete Laplacian, adjacency matrix, and signless…
We introduce quantum walks on Cayley graphs of non-Abelian groups. We focus on the easiest case of virtually Abelian groups, and introduce a technique to reduce the quantum walk to an equivalent one on an Abelian group with coin system…
In a recent work by Novo et al. (Sci. Rep. 5, 13304, 2015), the invariant subspace method was applied to the study of continuous-time quantum walk (CTQW). The method helps to reduce a graph into a simpler version that allows more…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…
We consider the quantum search problem with a continuous time quantum walk for networks of finite spectral dimension d_{s} of the network Laplacian. For general networks of fractal (integer or non-integer) dimension d_{f}, for which in…
This paper presents a quantum algorithm for triangle finding over sparse graphs that improves over the previous best quantum algorithm for this task by Buhrman et al. [SIAM Journal on Computing, 2005]. Our algorithm is based on the recent…
The quantum SearchRank algorithm is a promising tool for a future quantum search engine based on PageRank quantization. However, this algorithm loses its functionality when the $N/M$ ratio between the network size $N$ and the number of…
Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms…
The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph. We analytically prove that lackadaisical quantum walks can find a unique marked vertex on any regular…
We study continuous-time quantum walks mimicking the quantum search based on Grover's procedure. This allows us to consider structures, that is, databases, with arbitrary topological arrangements of their entries. We show that the…
This paper deals with the problem of the requirements for quantum systems that enable one to design efficient quantum algorithms. We rise the issue of the possibility to utilise the non-complete networks for algorithmic purposes. In…
We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric…