Research On Multiphase Grover Quantum Search Algorithms

Grover quantum search algorithm is an exhaustive algorithm on quantum computer,which achieves quadratic speed-up when searching in an unordered database.However,the probability of obtaining correct results usually decreases as the quantity of target increases,which is named multi-target deficiency in this paper.Multiphase Grover algorithms are the solutions which are able to amend this deficiency so that they draw extensive attentions.This paper is concentrated on multiphase Grover algorithms,and the main contributions are as the following three parts:1.A model of multiphase Grover algorithm is proposed in this paper,and existent multiphase Grover algorithms are demonstrated to be equivalent base on this model.Firstly,the unitary of the operators in this model is analyzed,then a four-phase improvement of Grover algorithm is proposed based on the model,whose phase-matching condition is also proposed.A multi-target quantum searching algorithm is designed according to the algorithm,when the proportion of correct results is over 1/3,the probability of getting correct results is greater than 97.82%with only one iteration.Then the relationship of existent multiphase Grover algorithms is researched.When phases meet the condition?=2?-??28???28???28?-?,these five algorithms are equivalent.Next,an instance is set up to show that extensive conclusions of one algorithm can be parallelly generalized to other algorithms through the equivalence,which will help to avoid repetitive researches.2 Quantum coherence,quantum entanglement and quantum discord in multiphase Grover algorithms are researched,and the impact of changeable phases on these quantum resources are mainly studied.By analyzing the relationship between quantum coherence and the number of iteration,searching probability and the number of iteration on the condition that phases are different,we obtained that the consumption of quantum coherence will enhance the searching success probability in multiphase Grover algorithms,and different phases will influence the rate of consumption of quantum coherence and enhancement of searching probability.Then an optimal phase in given conditions of multiphase Grover algorithms is obtained by analyzing the quantum coherence.This method offers a new thinking for the choice of optimal phase in multiphase Grover algorithms.Next,quantum entanglement and quantum discord in multiphase Grover algorithms are researched.It turned out that there are no direct connections between the enhancement of searching probability and consumption of quantum entanglement as well as quantum discord,and different phases will have an impact on the change rate of quantum entanglement and quantum discord in the operation of the algorithm.3.Quantum signature protocol based on multiphase Grover algorithms is researched.Firstly,the existent quantum signature protocol based on Grover algorithm by Chun et al.is introduced briefly,and the forge attack to this protocol is also introduced.Then,the principle that multiphase Grover algorithms to be utilized to design a quantum signature protocol is analyzed.Next,a quantum signature protocol based on multiphase Grover algorithm is proposed,whose quantum signature is designed by twice multiphase Grover iterations,and the safety of quantum signature in transmission is ensured,however,the secret key k_AB between Alice and Bob need to be known by the third party TC.Then a quantum digital signature protocol based on multiphase Grover algorithm and QOTP is proposed,the safety of quantum signature in transmission is ensured by QOTP,and k_AB needn't to be known by the third party TC.The two protocols mentioned above both sign the message bite by bite,so that they are easier in implementation than Chun's protocol,and they both meet correctness,non-repudiation and unforgeability.