Related papers: Multipartite entanglement and Grover's search algo…
We calculate the amount of entanglement of the multiqubit quantum states employed in the Grover algorithm, by following its dynamics at each step of the computation. We show that genuine multipartite entanglement is always present.…
Quantum Algorithms have long captured the imagination of computer scientists and physicists primarily because of the speed up achieved by them over their classical counterparts using principles of quantum mechanics. Entanglement is believed…
In this paper we investigate the entanglement nature of quantum states generated by Grover's search algorithm by means of algebraic geometry. More precisely we establish a link between entanglement of states generated by the algorithm and…
We investigate the entanglement features of the quantum states employed in quantum algorithms. In particular, we analyse the multipartite entanglement properties in the Deutsch-Jozsa, Grover and Simon algorithms. Our results show that for…
Grover's quantum search algorithm is analyzed for the case in which the initial state is an arbitrary pure quantum state $|\phi>$ of $n$ qubits. It is shown that the optimal time to perform the measurement is independent of $| \phi>$,…
Evolution of entanglement with the processing of quantum algorithms affects the outcome of the algorithm. Particularly, the performance of Grover's search algorithm gets worsened if the initial state of the algorithm is an entangled one.…
We investigate the issue of speed-up and the necessity of entanglement in Grover's quantum search algorithm. We find that in a pure state implementation of Grover's algorithm entanglement is present even though the initial and target states…
The Groverian entanglement measure introduced earlier for pure quantum states [O. Biham, M.A. Nielsen and T. Osborne, Phys. Rev. A 65, 062312 (2002)] is generalized to the case of mixed states, in a way that maintains its operational…
Evolution of entanglement with the proceeding of quantum algorithms affects the outcome of the algorithm. Particularly, the performance of Grover's search algorithm gets worsened if the initial state of the algorithm is an entangled one.…
Although entanglement is widely considered to be necessary for quantum algorithms to improve on classical ones, Lloyd has observed recently that Grover's quantum search algorithm can be implemented without entanglement, by replacing…
Grover's search algorithm is the optimal quantum algorithm that can search an unstructured database quadratically faster than any known classical algorithm. The role of entanglement and correlations in the search algorithm have been studied…
We analyze the role played by entanglement in the dynamical evolution of Grover's search algorithm in the space of qubits. We show that the algorithm can be equivalently described as an iterative change of the entanglement between 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…
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…
We study the entanglement content of the states employed in the Grover algorithm after the first oracle call when a few searched items are concerned. We then construct a link between these initial states and hypergraphs, which provides an…
Entanglement is considered to be one of the primary reasons for why quantum algorithms are more efficient than their classical counterparts for certain computational tasks. The global multipartite entanglement of the multiqubit states in…
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…
The entanglement of a quantum system can be valuated using Mermin polynomials. This gives us a means to study entanglement evolution during the execution of quantum algorithms. We first consider Grover's quantum search algorithm, noticing…
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…
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…