Spatial search by continuous-time quantum walks on renormalized Internet networks

Joonas Malmi, Matteo A. C. Rossi, Guillermo García-Pérez, Sabrina Maniscalco

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
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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 O(N), but it does not reach the ideal quadratic speedup O(√N) 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 99th percentile ordered according to the degree.
Original languageEnglish
Article number043185
Pages (from-to)1-10
Number of pages10
JournalPHYSICAL REVIEW RESEARCH
Volume4
Issue number4
DOIs
Publication statusPublished - 13 Dec 2022
MoE publication typeA1 Journal article-refereed

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