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Grover's algorithm for quantum searching of a database is generalized to deal with arbitrary initial amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the r marked and N-r…
This paper discusses an improvement to Grover's algorithm for searches where target states are Hamming weight eigenstates and search space is not ordered. It is shown that under these conditions search efficiency depends on the smaller…
Sparse quantum state preparation is a common subroutine in quantum algorithms, where classical data with few nonzero entries must be loaded into a quantum state. In this work, we consider the Grover-Rudolph algorithm, which has recently…
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…
In the Grover-type quantum search process a search operator is iteratively applied, say, k times, on the initial database state. We present an additive decomposition scheme such that the iteration process is expressed, in the computational…
In this work we address two questions concerning Grover's algorithm. In the first we give an answer to the question how to employ Grover's algorithm for actual search over database. We introduce a quantum model of an unordered phone book…
Grover's search algorithm has attracted great attention due to its quadratic speedup over classical algorithms in unsorted database search problems. However, Grover's algorithm is inefficient in multi-target search problems, except in the…
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…
We invoke an efficient search algorithms as a key challenge in multi-qubit quantum systems. An original algorithm called dynamical quantum search algorithm from which Grover algorithm is obtained at a specified time is presented. This…
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 represented by a basis state in the…
It is found that Grover's quantum search algorithm is not robust against phase inversion and Hadmard transformation inaccuracies. Imperfect phase inversions and Hadmard-Walsh transformations in Grover's quantum search algorithm lead to…
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…
In this paper, we study decoherence in Grover's quantum search algorithm using a perturbative method. We assume that each two-state system (qubit) that belongs to a register suffers a phase flip error (\sigma_{z} error) with probability p…
We firstly investigate the multipartite entanglement features of the quantum states, including the iteration states achieved by repeated application of Grover iteration and the Oracle ones into which the above iteration states evolve by…
When applying Grover's algorithm to an unordered database, the probability of obtaining correct results usually decreases as the quantity of target increases. To amend the limitation, numbers of improved schemes are proposed. In this paper,…
We propose a potentially practical scheme for realization of an n-qubit (n>2) conditional phase flip (CPF) gate and implementation of Grover search algorithm in the ion-trap system. We demonstrate both analytically and numerically that, our…
In this paper we present a search algorithm that finds useful optical quantum states which can be created with current technology. We apply the algorithm to the field of quantum metrology with the goal of finding states that can measure a…
Generalized Grover's searching algorithm for the case in which there are multiple marked states is demonstrated on a nuclear magnetic resonance (NMR) quantum computer. The entangled basis states (EPR states) are synthesized using the…
We demonstrate the implementation of Grover's quantum search algorithm on a liquid state nuclear magnetic resonance (NMR) quantum computer using essentially pure states. This was achieved using a two qubit device where the initial state is…
We want to find a marked element out of a black box containing N elements. When the number of marked elements is known this can be done elegantly with Grover's algorithm, a variant of which even gives a correct result with certainty. On the…