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

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Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2022-12-13
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Language
en
Pages
10
1-10
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PHYSICAL REVIEW RESEARCH, Volume 4, issue 4
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.
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Malmi , J , Rossi , M A C , García-Pérez , G & Maniscalco , S 2022 , ' Spatial search by continuous-time quantum walks on renormalized Internet networks ' , PHYSICAL REVIEW RESEARCH , vol. 4 , no. 4 , 043185 , pp. 1-10 . https://doi.org/10.1103/PhysRevResearch.4.043185
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