Research And Application Of Quantum Walk Algorithm On Finite Graphs

With the advent of the big data time,the research on the security of private information has gradually become the focus of the development of network information technology.Researchers at home and abroad have proposed many methods to protect privacy information,among which anonymous quantum communication is one of the important ways to protect information security.In the process of anonymous communication,the security of identity information of both parties is an important standard for the security of anonymous communication.However,the further development of anonymous quantum communication is severely restricted by the problems of privacy information disclosure and noise influence.In this paper,we study the quantum walk algorithm on finite graph and apply the algorithm to reduce the leakage of privacy information in anonymous communication.The quantum walk algorithm simulates the evolution of quantum coherence of particles moving on graphs.And quantum walk algorithm has randomness,which is applied in the field of anonymous quantum communication to protect the security of privacy information.Based on the two-lattice Bose-Hubbard model,the quantum walk algorithm is improved to reduce the impact of noise and increase the accuracy of searching algorithm.Continuous expansion based on the quantum discrete cosine transform.The continuous extended quantum cosine transform operator is constructed by the evolution operator of the quantum walk algorithm to compress the quantum information and improve the efficiency of information transmission.The main research contents of this paper are as follows:1.Aiming to the problem of identity leakage of both parties in communication,this paper designs an anonymous communication scheme based on quantum walk on finite graph by using the randomness of quantum walk.The evolution operator of the quantum walk algorithm is constructed by a trusted third party based on finite graph.The position probability distribution function of the receiver is calculated,and the value corresponding to its maximum value is defined as the target position and sent to the sender.The sender sends the transmission information at a fixed point according to the target position,and the receiver walks to search for the transmission information according to its initial state and evolution operator.The receiver uses the evolution operator to search and transmit the information in a stroll,which prevents the privacy information from being eavesdropped in the process of anonymous communication.2.Aiming to the problem that the quantum walk algorithm is affected by noise,which leads to the reduction of search accuracy.In this paper,a quantum walk error correction algorithm based on two-lattice Bose-Hubbard model is presented.According to the property of Bose-Hubbard model that no new particles can be generated by any substitution of two particles,quantum swap gate is constructed to exchange entangled particles.The model lattice is encoded with error correction,and the wandering particles are exchanged to the lattice with error correction coding by swap gate.To realize the quantum walk error correction under the open system and improve the accuracy of the algorithm.3.Aiming to the problem of low communication efficiency in anonymous quantum communication,a quantum information compression algorithm based on quantum continuous cosine transform is proposed in this paper.Fourier transform is used to transform discrete quantum information states into continuous quantum states.The search operator of Grover algorithm is constructed according to the discrete time quantum walk algorithm,and the auxiliary quantum state and operator are added to generate the quantum discrete cosine transform operator.After the continuous expansion of the discrete cosine transform operator,the continuous expansion quantum cosine transform operator is constructed to compress the continuous quantum state.This paper aims to study the quantum walk algorithm on finite graphs to improve the identity security and information transmission efficiency of both parties in anonymous communication.Through the above operation,the anonymous quantum communication between the two parties can avoid eavesdropping with great probability,reduce the influence of noise in the system when searching for transmitting information,and improve the efficiency of information transmission.