Unveiling Quantum Gates through Graph Theoretical Modelling: Exploring Single - Qubit Rotation Operators and Their Interplay with Linear Graph Theory

This paper implicates the graph theoretic approach for quantum information systems modelling by employing linear graph theoretic modelling to analyse single qubit rotation operator gates. By representing qubit states as nodes and rotation operations at edges, a linear graph framework is developed to systematically examine the interactions and transformations involved in qubit rotation. This study establishes a link between linear graph theory and quantum computing. Through this perspective, the paper contributes to both the fields of linear graph theoretic modelling of general systems and quantum computing, paving the way for new insights and advancements in quantum algorithm design and optimization.