New quantum approach can develop faster algorithm for complex networks, There is no shortage of complex networks in our world, from cellular networks in biology to complex networks in technology.
This network also forms the basis for various applications in almost all fields of science. A special search algorithm is needed to analyze and manipulate this network.
However, conventional search algorithms are slow and take a long time to work with large networks.
It was recently discovered that search algorithms based on the principles of quantum mechanics are clearly superior to the classical approach. One example is the “walking quantum” algorithm, which can be used to find a particular point or “tip” from an N-site graph.
Instead of just going through a neighboring peak, the quantum walking approach uses probabilistic estimates based on the theory of quantum mechanics, which drastically reduces the number of steps needed to find targets. New quantum approach can develop faster algorithm for complex networks.
To achieve this, an operation called “oracle call” must be carried out before the transition from one point to another to adjust the probability value in the representation of the quantum system.
One of the main problems is understanding the relationship between optimal oracle call computing time and network structure, because this connection is well understood for standard forms and bodies, but remains unclear for complex networks.
Scientists first examine the “fractal properties” (geometric properties of numbers that appear to reproduce infinitely whole shapes) in tissue.
For this purpose, they carried out numerical simulations with more than one million peaks and confirmed that the results were consistent with previous research that suggested mathematical laws or “scaling laws” to explain this relationship.
The researchers found that the scaling laws for some fractal grids varied according to their spectral dimensions, which confirmed previous assumptions for other grids.
Surprisingly, they even found that the scaling law for other types of fractal grids depends on the combination of intrinsic properties, which in turn shows that the previous assumptions about the optimal number of oracle calls can be true.
The question remains why this combination provides a scaling law for the number of Oracle calls. With this understanding, the team even proposed a new scaling hypothesis that was slightly different from the one previously proposed to provide deeper insight into the various fractal geometries of the network. New quantum approach can develop faster algorithm for complex networks.
The research team hopes that their results will make quantum search easier for experimental analysis – especially with new experiments that carry out quantum migrations in physical systems such as optical gratings.
The broad application of quantum algorithms to fractal grids underlines the importance of this research. The researchers say: We hope that our research will further promote interdisciplinary investigations of complex networks, mathematics and quantum mechanics on fractal geometry.