Study Of Quantum Hypergraph States

Quantum computing is a new calculations, according to theory of quantummechanics, the basis and principles of quantum computing and quantum algorithms isimportant in the speed of the calculation beyond the Turing machine model offers thepossibility, so quantum calculation than the classical quantum computing has a naturaladvantage. Since the concept of quantum compute and quantum information is putforward, the theory of quantum compute and quantum information was interested bycomputer scientists, physicists and mathematicians which is rapid developed.Quantum entanglement in which has a particularly important role, is one of the coreresearch in quantum computing and quantum information. The study of quantumentanglement, for the general state of multipartite systems, is more difficult tocalculate, and calculate some special status category, such as GHZ state, W state andstabilizer states and Figure states and so on, may be easier, which prompted us studythe special entanglement states.Ionicioiu and Spiller have in recently presented an axiomatic framework thatis for mapping graphs to quantum states of a suitable physical system. In this way,graphs can be encoded into the quantum state, which are graph states. After this, theseframeworks have been extended to the directed graph and weighted chart, andinvestigated their Entanglement and properties. As Figure with visualization ofadvantages, such as for the study of the nature of the state of entanglement is moreconvenient. So we consider promoting the state of graph to the state of hypergraphs sothat we can describe more quantum states.Hypergraph as promotion of graph, code it to its quantum state is very natural, onthe one hand, it provides a new ways of using theoretical of hypergraph to studyquantum entanglement; on the other hand, it also provides a new ideas that the use ofultra-quantum theory to investigate Figure issues. In this paper, based on theirfindings, we first generalize these axiomatic frameworks to encode hypergraph intoquantum states. Then we define a new group of quantum states of n qubits, named bythe hypergraph states, by using the above axiomatic approach. Further, we researchtranslate the actions of some local operations on hypergraph states into the transformson their corresponding hypergraphs and investigate some properties of multipartite entanglement of hypergraph states, and their entanglement with Schmidt metricmethods for the quantitative. In the last of this article, we study the relations betweenhypergraph states and real equal weights states, the relations of hypergraph state,graph states and stabilizer states.