Related papers: Unstructured Search by Random and Quantum Walk
The rapid progress of computer science has been accompanied by a corresponding evolution of computation, from classical computation to quantum computation. As quantum computing is on its way to becoming an established discipline of…
We study the quantum walk search algorithm of Shenvi, Kempe and Whaley [PRA 67 052307 (2003)] on data structures of one to two spatial dimensions, on which the algorithm is thought to be less efficient than in three or more spatial…
We investigate optimizing quantum tree search algorithms by employing a nested Grover Algorithm. This approach seeks to enhance results compared to previous Grover-based methods by expanding the tree of partial assignments to a specific…
We develop a general theory for a quantum-walk search on a star graph. A star graph has N edges each of which is attached to a central vertex. A graph G is attached to one of these edges, and we would like to find out to which edge it is…
In this work we study quantum algorithms for Hopcroft's problem which is a fundamental problem in computational geometry. Given $n$ points and $n$ lines in the plane, the task is to determine whether there is a point-line incidence. The…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one…
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…
We present two new quantum algorithms that either find a triangle (a copy of $K_{3}$) in an undirected graph $G$ on $n$ nodes, or reject if $G$ is triangle free. The first algorithm uses combinatorial ideas with Grover Search and makes…
We treat a quantum walk model with in- and out- flows at every time step from the outside. We show that this quantum walk can find the marked vertex of the complete graph with a high probability in the stationary state. In exchange of the…
Quantum algorithms have demonstrated provable speedups over classical counterparts, yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge. In this work, we decode the quantum…
This paper describes a novel approach to solving unstructured search problems using a classical, signal-based emulation of a quantum computer. The classical nature of the representation allows one to perform subspace projections in addition…
The quantum search algorithm is a technique for searching N possibilities in only sqrt(N) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from…
This work considers a generalization of Grover's search problem, viz., to find any one element in a set of acceptable choices which constitute a fraction f of the total number of choices in an unsorted data base. An infinite family of…
We provide numerical evidence that the nonlinear searching algorithm introduced by Wong and Meyer \cite{meyer2013nonlinear}, rephrased in terms of quantum walks with effective nonlinear phase, can be extended to the finite 2-dimensional…
Recently, Ambainis gave an O(N^(2/3))-query quantum walk algorithm for element distinctness, and more generally, an O(N^(L/(L+1)))-query algorithm for finding L equal numbers. We point out that this algorithm actually solves a much more…
In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse…
Grover's quantum search algorithm provides a quadratic quantum advantage over classical algorithms across a broad class of unstructured search problems. The original protocol is probabilistic, returning the desired result with significant…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
The quantum search algorithm consists of an alternating sequence of selective inversions and diffusion type operations, as a result of which it can find a target state in an unsorted database of size N in only sqrt(N) queries. This paper…