Spatial search by continuous-time quantum walks on renormalized Internet networks
arXiv:2205.02137 · doi:10.1103/PhysRevResearch.4.043185
Abstract
We study spatial search with continuous-time quantum walks on real-world complex networks. We use smaller replicas of the Internet network obtained with a recent geometric renormalization method introduced by García-Pérez et al., Nat. Phys. 14, 583 (2018). This allows us to infer for the first time the behavior of a quantum spatial search algorithm on a real-world complex network. By simulating numerically the dynamics and optimizing the coupling parameter, we study the optimality of the algorithm and its scaling with the size of the network, showing that on average it is considerably better than the classical scaling , but it does not reach the ideal quadratic speedup that can be achieved, e.g. in complete graphs. However, the performance of the search algorithm strongly depends on the degree of the nodes and, in fact, the scaling is found to be very close to optimal when we consider the nodes below the th percentile ordered according to the degree.
11 pages, 6 figures
References in corpus (10)
- Hyperbolic Geometry of Complex Networks
- Universal computation by quantum walk
- Spatial search by quantum walk
- Sustaining the Internet with Hyperbolic Mapping
- Self-similarity of complex networks and hidden metric spaces
- Connectivity is a Poor Indicator of Fast Quantum Search
- Quadratic speedup for spatial search by continuous-time quantum walk
- On the optimality of spatial search by continuous-time quantum walk
- Continuous-time quantum walks on dynamical percolation graphs
- Continuous-time quantum walk spatial search on the Bollobás scale-free network