Holography of Transmission Lines: Insights of Continuous MERA and AdS/CFT

Abstract: This study examines the holographic representation of the quantum theory of transmission lines, which play a crucial role in quantum computing and quantum information. Utilizing Yurke and Denker's quantum circuit network theory within the framework of continuous MERA (cMERA) in AdS space, we analyze the quantization and interactions of transmission lines. The metric is revealed to be described by the inductance of the quantum circuit, which is AdS-space in its 0-limit. These results provide new insights into handling and controlling complex phenomena in quantum circuits, potentially advancing the understanding of quantum computing and quantum communication.