Study Of The Entanglement Of Quantum States In Grover Algorithm

Quantum computing and quantum information is a new interdisciplinary which is the combination of quantum mechanics and theoretical computer.The concept of quantum computer have been proposed in 1982.Since the basis and principles of quantum computing and quantum algorithms,quantum computer can efficiently solve some computational problems which have no efficient solution on a classical computer,or even a probabilistic Turing machine.The potential of quantum computer maks this theory develop rapidly,and was interested by physicists,mathematicians and computer scientists.In quantum circuit model,the quantum search algorithm is the more sophisticated algorithms.In the problem of conducting a search through some unstructured search space,grover search algorithm can be a quadratic speedup over the best classical one is shown.Tthe widespread applicability of search-based method-logies has caused a big attation of people to Grover algorithm.Such a mature quantum algorithms display that quantum computers with the appropriate quantum algorithms for some NP classical computer to accelerate,which has great significance.And to identify the key causes of accelerated that quantum algorithms has done in NP problems,quantum,and has meaningful significance in proposal more new quantum algorithms.Quantum entanglement is an important feature in quantum computing?Generally,it is believed that the study of quantum entanglement can better understand the meaning of quantum mechanics,more conducive to the development of new quantum algorithms.As for the general state of multi-systems,the calculation is very complex,and some special status is relatively easy.In summary,this article investigate the multipartite entanglement features of the quantum states by means of the separable degree and the entanglement measure.Then we give the qualitative and quantitative descriptions of the entanglement dynamics of the quantum states in Grover's search algorithm.We are trying to study the contribution of multipartite entanglement for the algorithm acceleration.In the Grover search algorithm,we also found a special kind of quantum state,namely hypergraph state.Hypergraph states is also a special status of multi-system,it established a bridge between hypergraph and quantum states.Use the entanglement properties of hypergraph states,we can not only help us to use quantum theory to solve hypergraph problems,but also allows us to study new quantum entanglement use hypergraph theory.We first introduce an approach for computing the concurrence between two specific qubits of a hypergraph state by using the so-called Hamming weights of several special subhypergraphs of the corresponding hypergraph.Then we quantify and characterize bipartite entanglement between each qubit pair of several special hypergraph states in terms of the concurrence obtained by using the above approach.