Modeling of optical conductivity of networks with full binary encoding

Optical conductivity is the most important characteristic of graphs. It is a special case of continuous quantum walks on a graph and depends both on the structure of the graph and on the characteristics of the waveguides that are its edges. We investigated the conductivity of optical networks whose vertices have binary encoding depending on the thickness and length of the waveguides. It is found that the conductivity drops to zero with increasing graph size at different distributions of waveguide characteristics, which contrasts with random walks on a straight line, where such an effect does not occur. This effect has a purely interference nature and manifests itself precisely for graphs whose encoding contains all binary sets. More subtle dependences of conductivity on the characteristics of waveguides are also established. This result can be useful when choosing the structure of optical nanodevices of large sizes, for example, for optical quantum computers.