Related papers: Entanglement in the Grover's Search Algorithm
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…
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…
L. K. Grover's search algorithm in quantum computing gives an optimal, square-root speedup in the search for a single object in a large unsorted database. In this paper, we expound Grover's algorithm in a Hilbert-space framework that…
Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. The growth of entanglement is a major challenge for classical simulation methods. In this work, we…
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…
Grover's algorithm constitutes the optimal quantum solution to the search problem and provides a quadratic speed-up over all possible classical search algorithms. Quantum interference between computational paths has been posited as a key…
We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…
In this article, we present a novel approach to investigating entanglement in the context of quantum computing. Our methodology involves analyzing reduced density matrices at different stages of a quantum algorithm's execution and…
Calibrating the role of entanglement in quantum algorithms is a crucial task in the development of quantum computing. Most existing studies have primarily focused on how the static properties of entanglement-such as its magnitude and…
The Grover search algorithm performs an unstructured search of a marked item in a database quadratically faster than classical algorithms and is shown to be optimal. Here, we show that if the search space is divided into two blocks with the…
With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple…
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…
Grover's algorithm, orginally conceived as a means of searching an unordered database, can also be used to extract solutions from the result sets generated by quantum computations. The Grover algorithm exploits the concept of an oracle…
The question of which resources drive the advantages in quantum algorithms has long been a fundamental challenge. While entanglement and coherence are critical to many quantum algorithms, our results indicate that they do not fully explain…
We demonstrate that, in the case of Shor's algorithm for factoring, highly mixed states will allow efficient quantum computation, indeed factorization can be achieved efficiently with just one initial pure qubit and a supply of initally…
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…
The Grover algorithm is a crucial solution for addressing unstructured search problems and has emerged as an essential quantum subroutine in various complex algorithms. By using a different approach with previous studies, this research…
The Grover quantum search algorithm is generalized to deal with an arbitrary mixed initial state. The probability to measure a marked state as a function of time is calculated, and found to depend strongly on the specific initial state. The…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…