The Universal Modeling Of Quantum Computing Based On Quantum Walk

Quantum walk is an effective tool to study quantum algorithm, as well as to construct the general modeling of quantum computation. At present, the quantum walk as an important direction in the research field of quantum computation, has obtained important development in both quantum physics and computing science. This paper will discuss the theories of both the coined discrete quantum walk and continuous quantum walk, the foundation of mathematical modeling of quantum walk, the inherent randomness and quantumness in quantum walk, the mathematical corresponding between the coined discrete quantum walk and continuous quantum walk, the topological structures of graphs associated by quantum walk, and some other aspects.Thus, we discuss the versatility of quantum walk model description, and discrete quantum walk on quantum algorithms scenario, search, halt problem, and several other famous triangle judgment decision problem, since that the decision problem is entirely the problem, which can apparently come to a universal quantum algorithm design methodology. This paper focuses on the subsequent continuous quantum walk on to construct universal quantum computing models, and decision problems on graph theory for the docking of two abstract tree between leaf nodes, then the tree structure, discussed in the course of the Hamiltonian operators with energy E and the transit coefficient T(E), and the mathematical relationship between them. Then we give the function graph, discussing the algorithm efficiency.At the late part of this paper, we will show a picture for depicting the future of quantum computer on engineering realization. According to the two kinds of modeling of quantum walk, it will develop both high-level and the low-level programming language respectively to facilitate the understanding of both the mankind thought and the quantum machine.