量子有记忆漫步通用模型的研究与分析

Quantum computing, a new method of computing, has outstanding computing power. Considering the fact that quantum walk is an important model which could realize quantum computing, the research of quantum walks is meaningful with full of research value. Quantum walks with memory is a kind of modified quantum walks, which is more flexible than normal quantum walks. On the basis of generic quantum walks with memory on regular graphs, this project will study generic quantum walks with memory from the following three aspects: 1.research on properties of generic quantum walks with memory on regular graphs; 2. research on generic model of quantum walks with memory as an open quantum system; 3. construction of Szegedy, Staggered generic quantum walks with memory and investigation of relation between coin, Szegedy, Staggered generic quantum walks with memory. Through the study of this project, we will establish three types of generic quantum walks with memory and gain comprehensive analysis results of quantum walks with memory. This project will provide theoretical basis for constructing quantum algorithms based on quantum walks with memory. In addition, this project will expand the platform for quantum computing.

量子计算作为新兴的计算方式，拥有卓越的计算能力。量子漫步作为实现量子计算的重要模型之一，具有重要的理论意义和研究价值。量子有记忆漫步是修正的量子漫步，具有更高的灵活性。本项目在构建出正则图上硬币型量子有记忆漫步通用模型的基础上，研究与分析量子有记忆漫步通用模型，具体研究内容如下： 1.正则图上的量子有记忆漫步通用模型性质研究；2.量子有记忆漫步作为开放量子系统的模型研究；3. Szegedy型和Staggered型量子有记忆漫步的通用模型构建及两者与硬币型之间的相互联系。本项目的研究，构建出了三种形式量子有记忆漫步通用模型，并对其进行了全面的研究与分析，为构建基于量子有记忆漫步的量子算法提供坚实的理论基础，拓展了量子算法的实现平台。

量子计算作为新兴的计算方式，拥有卓越的计算能力。量子漫步作为实现量子计算的重要模型之一，具有重要的理论意义和研究价值。量子有记忆漫步是修正的量子漫步，具有更高的灵活性。本研究在构建出正则图上硬币型量子有记忆漫步通用模型的基础上，研究与分析量子有记忆漫步通用模型，具体研究内容如下： 1.构建了两种正则图上的量子有记忆漫步模型，并对其各方面性质进行了全面的研究；2.研究了量子有记忆漫步作为开放量子系统时的Kraus算子的变化；3. 多种形式的量子有记忆漫步的通用模型构建及他们之间的相互联系。本研究构建出了多种形式量子有记忆漫步通用模型，并对其进行了全面的模型研究与性质分析，为构建基于量子有记忆漫步的量子算法提供坚实的理论基础，拓展了量子算法的实现平台。