In the dynamic field of quantum computing, efficient construction of Matrix Product Operators (MPOs) and Tree Tensor Network Operators (TTNOs) plays a pivotal role in understanding complex quantum systems. This project embarks on an approach by applying bipartite graph theory to optimize the construction of MPOs and extending this methodology to TTNOs, a domain where such an application is unprecedented. Initially, the study meticulously reevaluates an existing algorithm for constructing MPOs through bipartite graphs, confirming its validity and efficiency. The transition to TTNOs unveiled significant challenges, necessitating considerable modifications to the algorithm. Despite these obstacles, an optimal construction for TTNOs was achieved, marking a significant advancement in the field. The report details the methodological evolution, from theoretical underpinnings to practical implementation, and underscores a new algorithm to create optimal TTNOs.     «

In the dynamic field of quantum computing, efficient construction of Matrix Product Operators (MPOs) and Tree Tensor Network Operators (TTNOs) plays a pivotal role in understanding complex quantum systems. This project embarks on an approach by applying bipartite graph theory to optimize the construction of MPOs and extending this methodology to TTNOs, a domain where such an application is unprecedented. Initially, the study meticulously reevaluates an existing algorithm for constructing MPOs t...     »