The Application Of Discrete Quantum Walk In Spatial Search And Quantum Hash Function Construction

Quantum walk is the quantum counterpart of classical random walk.It is a new type of quantum computation model proposed in recent years.Discrete quantum walk is the base of constructing many quantum algorithms,so it has attracted the attention of scholars in the world.At present,foreign scholars have conducted extensive and in-depth researches on the topological properties of quantum walks,localization of Anderson,applications and experiments.Many domestic scholars including Professor XUE Peng of the Department of Physics of Southeast University have also conducted researches in these aspects and have achieved a lot of important results.These research results have important effects on condensed matter physics and fault-tolerant quantum computation.However,these researched are limited to the domain of quantum.Although significant research progress has been made in hardware and software of quantum computing at home and abroad,the universal and practical quantum computer has not been realized,which greatly limits the practical application of quantum walk model.In view of this,this paper studies discrete quantum walk and its application in quantum Hash function and space search from macro and micro aspects.The main work and innovation of this paper are as follows:(1)Based on discrete quantum walk,we proposed an efficient Hash function using the dense coding technique of coin operator.Compared with the existing quantum Hash functions,our protocol has a doubled efficiency and even more.Only one coin operator is needed to meet the requirement of the protocol without the interaction between the two operators.At the same time,we proposed a dense coding technique for coin operators,which can be extended to the case where m(m>2)message bits control the coin operator in each iteration.(2)We constructed the theoretical formula of quantum walk in three-dimensional space.We also derived a discrete-time-quantum-walk-based search algorithm based on the standard quantum walk formula which can significantly increase the quantum walk probability to a specified position.(3)Based on the designed quantum walk search algorithm in three-dimensional space,we completed the design of TDQW simulation software,which can realize the compression of messages by Hash function.It can be used for 3D dynamic visualization simulation of quantum walking and searching in hypercube and three-dimensional space,allowing users to observe the entanglement evolution of coins and walkers on various time scales through the Von Neumann entropy of coins.It can also provide the basis for the research of quantum-walk-based algorithms and physical system modeling using quantum walk.