Unveiling the Importance of Non-Shortest Paths in Quantum Networks

• URL: http://arxiv.org/abs/2402.15462v4
• Date: Thu, 19 Dec 2024 15:47:10 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 apply a statistical physics model -- concurrence percolation -- to uncover the origin of stronger connectivity on scale-free networks. Our findings highlight a crucial principle for QN design: when non-shortest paths are abundant, they notably enhance QN connectivity beyond what is achievable with classical percolation.
• Score: 1.3350320201707588
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• Abstract: Quantum networks (QNs) exhibit stronger connectivity than predicted by classical percolation, yet the origin of this phenomenon remains unexplored. Here, we apply a statistical physics model -- concurrence percolation -- to uncover the origin of stronger connectivity on hierarchical scale-free networks, the ($U,V$) flowers. These networks allow full analytical control over path connectivity through two adjustable path-length parameters, $U \leq V$. This precise control enables us to determine critical exponents well beyond current simulation limits, revealing that classical and concurrence percolations, while both satisfying the hyperscaling relation, fall into distinct universality classes. This distinction arises from how they "superpose" parallel, non-shortest path contributions into overall connectivity. Concurrence percolation, unlike its classical counterpart, is sensitive to non-shortest paths and shows higher resilience to detours as these paths lengthen. This enhanced resilience is also observed in real-world hierarchical, scale-free Internet networks. Our findings highlight a crucial principle for QN design: when non-shortest paths are abundant, they notably enhance QN connectivity beyond what is achievable with classical percolation.

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