Unveiling the Importance of Non-Shortest Paths in Quantum Networks

• URL: http://arxiv.org/abs/2402.15462v2
• Date: Wed, 21 Aug 2024 00:42:53 GMT
• Title: Unveiling the Importance of Non-Shortest Paths in Quantum Networks
• Authors: Xinqi Hu, Gaogao Dong, Renaud Lambiotte, Kim Christensen, Jingfang Fan, Zihao Tian, Jianxi Gao, Shlomo Havlin, Xiangyi Meng,
• Abstract summary: We find that concurrence percolation relies on non-shortest paths and shows a higher resilience to detouring when these paths are rerouted and extended. Our findings highlight a critical principle for QN design: non-shortest paths contribute significantly to QN connectivity compared to classical percolation.
• Score: 1.3350320201707588
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The advancement of large-scale quantum technologies necessitates a deeper understanding of the quantum network (QN) design from first principles. Pioneering studies, however, do not fully capture the origin of the stronger connectivity in QN that surpasses classical percolation predictions. Here, we apply statistical physics to identify the origin of this stronger connectivity -- known as concurrence percolation. Our finding is demonstrated on hierarchical scale-free networks, the ($U,V$) flowers, which allow full analytical control over path connectivity by adjusting the two distinct path length scales, $U \leq V$. This advantage enables us to analytically determine the critical exponents for infinite systems well beyond the current simulation limits. Our analysis reveals for the first time that classical and concurrence percolations, while both satisfying the hyperscaling relation, fall into distinct universality classes. This distinction arises from their different methods for how to ``superpose'' parallel, non-shortest path contributions into overall connectivity. Notably, we find that concurrence percolation relies on non-shortest paths and shows a higher resilience to detouring when these paths are rerouted and extended. This increased resilience is also evident in real-world hierarchical, scale-free Internet networks. Our findings highlight a critical principle for QN design: non-shortest paths contribute significantly to QN connectivity compared to classical percolation -- as long as they are abundant.

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