Related papers: Generalization of Grover's Algorithm to Multiobjec…

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…

Database search has wide applications and is used as a subroutine in many important algorithms. We shall consider a database with one target item. Quantum algorithm finds the target item in a database faster than any classical algorithm. It…

We show that Grover's algorithm defines a geodesic in quantum Hilbert space with the Fubini-Study metric. From statistical point of view Grover's algorithm is characterized by constant Fisher's function. Quantum algorithms changing…

Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification…

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…

We generalize Grover algorithm with two arbitrary phases in a density matrix set up. We give exact analytic expressions for the success probability after arbitrary number of iteration of the generalized Grover operator as a function of…

Generic quantum search algorithm searches for target entity in an unsorted database by repeatedly applying canonical Grover's quantum rotation transform to reach near the vicinity of the target entity. Thus, upon measurement, there is a…

Grover's algorithm is a fundamental quantum algorithm that offers a quadratic speedup for the unstructured search problem by alternately applying physically implementable oracle and diffusion operators. In this paper, we reformulate the…

This paper presents an enhancement to Grover's search algorithm for instances where the number of items (or the size of the search problem) $N$ is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum…

We solve the unstructured search problem in constant time by computing with a physically motivated nonlinearity of the Gross-Pitaevskii type. This speedup comes, however, at the novel expense of increasing the time-measurement precision.…

Some of the secret sharing schemes having unique quantum features like parallelism and entanglement are supposed to be relatively secure. Different schemes proposed by various researchers over the years have features which could be specific…

The operations of data set, such as intersection, union and complement, are the fundamental calculation in mathematics. It's very significant that designing fast algorithm for set operation. In this paper, the quantum algorithm for…

We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…

Distributed computing seems to be a natural approach to overcome size limitations of quantum computers in terms of number of qubits. But one lacks an efficient distribution approach to deal systematically with potential algorithms. This…

This paper is a written version of a one hour lecture given on Lov Grover's database search algorithm. Table Of Contents 1 ... Problem Definition 2 ... The quantum mechanical perspective 3 ... Properties of the inversion I_|psi> 4 ... The…

One of the most important quantum algorithms ever discovered is Grover's algorithm for searching an unordered set. We give a new lower bound in the query model which proves that Grover's algorithm is exactly optimal. Similar to existing…

Grover's unstructured search algorithm is one of the best examples to date for the superiority of quantum algorithms over classical ones. Its applicability, however, has been questioned by many due to its oracular nature. We propose a…

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…

We review the basic theoretical underpinnings of the Grover algorithm, providing a rigorous and well motivated derivation. We then present a generalization of Grover's algorithm that searches an arbitrary subspace of the multi-dimensional…

We propose a quantum algorithm for solving combinatorial search problems that uses only a sequence of measurements. The algorithm is similar in spirit to quantum computation by adiabatic evolution, in that the goal is to remain in the…