Related papers: Structured quantum search in NP-complete problems …
We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a…
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's…
Consider the unstructured search of an unknown number l of items in a large unsorted database of size N. The multi-object quantum search algorithm consists of two parts. The first part of the algorithm is to generalize Grover's…
Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example…
Grover's quantum search algorithm is considered as one of the milestone in the field of quantum computing. The algorithm can search for a single match in a database with $N$ records in $O(\sqrt{N})$ assuming that the item must exist in the…
Grover's algorithm is a quantum search algorithm that proceeds by repeated applications of the Grover operator and the Oracle until the state evolves to one of the target states. In the standard version of the algorithm, the Grover operator…
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…
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…
Quantum searching for one of $N$ marked items in an unsorted database of $n$ items is solved in $\mathcal{O}(\sqrt{n/N})$ steps using Grover's algorithm. Using nonlinear quantum dynamics with a Gross-Pitaevskii type quadratic nonlinearity,…
Withdrawn by the author due to irreparable errors. We present a quantum algorithm that in the black-box model performs a search in an ordered list of N elements. Using 3/4 log N + O(1) queries, it achieves a success probability of at least…
Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an $N$ element database require at most…
The use of superposition of states in quantum computation, known as quantum parallelism, has significant advantage in terms of speed over the classical computation. It can be understood from the early invented quantum algorithms such as…
Since Grover's seminal work, quantum search has been studied in great detail. In the usual search problem, we have a collection of n items and we would like to find a marked item. We consider a new variant of this problem in which…
Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…
In this work, we consider a family of sure-success quantum algorithms, which is grouped into even and odd members for solving a generalized Grover search problem. We prove the matching conditions for both groups and give the corresponding…
Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries…
Grover search is a renowned quantum search algorithm that leverages quantum superposition to find a marked item with quadratic speedup. However, when implemented on Noisy Intermediate-scale Quantum (NISQ) hardware, the required repeated…
The essential operations of a quantum computer can be accomplished using solely optical elements, with different polarization or spatial modes representing the individual qubits. We present a simple all-optical implementation of Grover's…
Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high…
Grover's quantum algorithm for an unstructured search problem and the Count algorithm by Brassard et al. are generalized to the case when the initial state is arbitrarily and maximally entangled. This ansatz might be relevant with quantum…