Related papers: No Infinite Tail Beats Optimal Spatial Search
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 spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers…
A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum…
We formulate Grover's unstructured search algorithm as a chiral quantum walk, where transitioning in one direction has a phase conjugate to transitioning in the opposite direction. For small phases, this breaking of time-reversal symmetry…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
Spatial data structures allow to make efficient queries on Geographical Information Systems (GIS). Spatial queries involve the geometry of the data, such as points, lines, or polygons. For instance, a spatial query could poll for the…
In a series of papers, Avraham, Filtser, Kaplan, Katz, and Sharir (SoCG'14), Kaplan, Katz, Saban, and Sharir (ESA'23), and Katz, Saban, and Sharir (ESA'24) studied a class of geometric optimization problems -- including reverse shortest…
We generalize Grover's unstructured quantum search algorithm to enable it to use an arbitrary starting superposition and an arbitrary unitary matrix simultaneously. We derive an exact formula for the probability of the generalized Grover's…
Given a simple graph $G$, we consider the node search problem with inert fugitive. We are interested in minimizing the maximum vertex occupation time, i.e. the maximum number of steps in which a vertex is occupied by a searcher during a…
Continuing the recent trend, in this article we design several space-efficient algorithms for two well-known graph search methods. Both these search methods share the same name {\it breadth-depth search} (henceforth {\sf BDS}), although…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…
We study the classical problem introduced by R. Isaacs and S. Gal of minimizing the time to find a hidden point $H$ on a network $Q$ moving from a known starting point. Rather than adopting the traditional continuous unit speed path…
This paper considers the collaborative graph exploration problem in GPS-denied environments, where a group of robots are required to cover a graph environment while maintaining reliable pose estimations in collaborative simultaneous…
Local search is a powerful heuristic in optimization and computer science, the complexity of which has been studied in the white box and black box models. In the black box model, we are given a graph $G = (V,E)$ and oracle access to a…
We present new intuition behind Grover's quantum search algorithm by means of a Hamiltonian. Given a black-box Boolean function f mapping strings of length n into {0,1} such that f(w) = 1 for exactly one string w, L. K. Grover describes a…
In a node-labeled graph, keyword search finds subtrees of the graph whose nodes contain all of the query keywords. This provides a way to query graph databases that neither requires mastery of a query language such as SPARQL, nor a deep…
We present a quantum algorithm for solving perfect mazes by casting the pathfinding task as a structured search problem. Building on Grover's amplitude amplification, the algorithm encodes all candidate paths in superposition and evaluates…
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…
We design quantum algorithms for maximum matching. Working in the query model, in both adjacency matrix and adjacency list settings, we improve on the best known algorithms for general graphs, matching previously obtained results for…