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Journal of Zunyi Normal College

Some Mathematical Results in Quantum Communication

Yong Wang

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

By the way of combinatorial computation, sequence of number and series knowledge, and the constructing proof methods, some mathematical results in quantum communication are solved, some equalities in quantum computation are proved. These results will be used in other sciences deeply.

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In this paper we show that every combinatorial problem has an exact explicit equation that returns its solution. We present a method to obtain an equation that solves exactly any combinatorial problem, both inversion, constraint satisfaction and optimization, by obtaining its equivalent tensor network. This formulation only requires a basic knowledge of classical logical operators, at a first year level of any computer science degree. These equations are not necessarily computable in a reasonable time, nor do they allow to surpass the state of the art in computational complexity, but they allow to have a new perspective for the mathematical analysis of these problems. These equations computation can be approximated by different methods such as Matrix Product State compression. We also present the equations for numerous combinatorial problems. This work proves that, if there is a physical system capable of contracting in polynomial time the tensor networks presented, every NP-Hard problem can be solved in polynomial time.
his study explores the application of quantum computing in solving complex mathematical problems through the utilization of Grover's Algorithm. Grover's Algorithm, renowned for its efficiency in unstructured search, has been adapted for various mathematical applications requiring rapid solution searches within large solution spaces. In this study, we implement Grover's Algorithm on a quantum computing platform to address a range of complex mathematical problems, including nonlinear equations and combinatorial optimization. Experimental results demonstrate that Grover's Algorithm significantly reduces computational time compared to classical methods, highlighting the immense potential of quantum computing in advanced mathematics. These findings pave the way for the development of more sophisticated quantum algorithms and their applications across science, engineering, and technology domains.
Being one of the major points of research focus since the end of the twentieth century, quantum computation technologies have experienced significant improvements and is under the progress of forming an inter-connected commercial quantum network in recent years. Communication through quantum mechanisms proved to be considerably more efficient and secure than classical communication protocols. Basic quantum communication networks have the primary composition of quantum processing nodes and channels where the interaction between the nodes is satisfied by the entanglement phenomenon. Quantum networking technology is under rapid development currently and is anticipated to receive milestone achievements shortly.