Related papers: Quantum spatial search on planar networks
We study a general model of random dynamical simplicial complexes and derive a formula for the asymptotic degree distribution. This asymptotic formula encompasses results for a number of existing models, including random Apollonian networks…
Spatially constrained planar networks are frequently encountered in real-life systems. In this paper, based on a space-filling disk packing we propose a minimal model for spatial maximal planar networks, which is similar to but different…
We examine the effect of network heterogeneity on the performance of quantum search algorithms. To this end, we study quantum search on a tree for the oracle Hamiltonian formulation employed by continuous-time quantum walks. We use…
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…
Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases…
We investigate the generalisation of quantum search of unstructured and totally ordered sets to search of partially ordered sets (posets). Two models for poset search are considered. In both models, we show that quantum algorithms can…
In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in $\mathbb{R}^2$, forming new connections to old nodes subject to the constraint that edges do not…
As the inevitable development trend of quantum key distribution, quantum networks have attracted extensive attention, and many prototypes have been deployed over recent years. Existing quantum networks based on optical fibers or quantum…
Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show…
Although strongly regular graphs and the hypercube are not complete, they are "sufficiently complete" such that a randomly walking quantum particle asymptotically searches on them in the same $\Theta(\sqrt{N})$ time as on the complete…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
With the growing interest in quantum machine learning, the perceptron -- a fundamental building block in traditional machine learning -- has emerged as a valuable model for exploring quantum advantages. Two quantum perceptron algorithms…
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work,…
Grover's quantum search algorithm can be formulated as a quantum particle randomly walking on the (highly symmetric) complete graph, with one vertex marked by a nonzero potential. From an initial equal superposition, the state evolves in a…
We investigate the behavior of the recently proposed quantum Google algorithm, or quantum PageRank, in large complex networks. Applying the quantum algorithm to a part of the real World Wide Web, we find that the algorithm is able to…
Quantum walks have been very successful in the development of search algorithms in quantum information, in particular in the development of spatial search algorithms. However, the construction of continuous-time quantum search algorithms in…
We present several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms. For these graphs, we construct quantum circuits that explicitly implement the full quantum walk…
Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…
We analyze the asymptotic properties of a Euclidean optimization problem on the plane. Specifically, we consider a network with three bins and $n$ objects spatially uniformly distributed, each object being allocated to a bin at a cost…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…