Quantum Coherence And Entanglement In Deutsch-jozsa Algorithm And Grover Search Algorithm

With the rapid development of the society and economic,the speed of information processing has been unable to meet the needs of the broad masses of the crowd,the speed of the traditional computer in all aspects of the upgrade is still unable to meet the current information processing speed.The improvement of performance and calculation speed of traditional computers still cannot meet the demands of information processing speed.The rapid development of quantum computers has brought new hope to this phenomenon.Different from traditional computers,quantum coherence and quantum entanglement and other characteristics bring parallel computing methods for quantum computing.It can be concluded that quantum coherence and quantum entanglement are essential to the development of quantum computer,and quantum entanglement is also an integral part of quantum mechanics.Quantum coherence,quantum entanglement,is an important resource of quantum information processing,which is widely studied in quantum information.The development of quantum computers depends on quantum algorithms,quantum coding,and so on,all related to quantum coherence and quantum entanglement.Therefore,it is meaningful to study quantum coherence and quantum entanglement in the process of quantum algorithm.In this paper,we introduce the definition of quantum coherence,entanglement,Deutsch-Jozsa algorithm,Grover search algorithm,we study the changes of quantum coherence in Deutsch-Jozsa algorithm and Grover search algorithm and changes of quantum entanglement in Deutsch-Jozsa algorithm and Grover search algorithm.In the Deutsch-Jozsa algorithm,the quantum coherence is studied in two cases:the equilibrium function and the normal function.Under the Deutsch-Jozsa algorithm,firstly we select the appropriate Hamilton and we study the quantum coherence in the l1-norm and relative entropy and show the expression of quantum coherence,eventually run out of the image in matlab and draw out the corresponding conclusion.We also study quantum coherence and quantum entanglement in the Grover search algorithm,and choose the appropriate Hamilton,take the same steps,draw out the final image.Compared to two kinds of algorithm of image,we draw out the final conclusions.We also study the variation of quantum entanglement in two algorithms,and the results show that the quantum coherence is decreased with the increase of the probability of success of the algorithm,while the quantum entanglement does not have this feature.Therefore,quantum coherence is the important resource of deutsh-jozsa algorithm and Grover search algorithm.