Topological network analysis using a programmable photonic quantum processor
Authors:
Shang Yu,
Jinzhao Sun,
Zhenghao Li,
Ewan Mer,
Yazeed K Alwehaibi,
Oscar Scholin,
Gerard J. Machado,
Kuan-Cheng Chen,
Aonan Zhang,
Raj B Patel,
Ying Dong,
Ian A. Walmsley,
Vlatko Vedral,
Ginestra Bianconi
Abstract:
Understanding topological features in networks is crucial for unravelling complex phenomena across fields such as neuroscience, condensed matter, and high-energy physics. However, identifying higher-order topological structures -- such as $k$-cliques, fundamental building blocks of complex networks -- remains a significant challenge. Here we develop a universal programmable photonic quantum proces…
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Understanding topological features in networks is crucial for unravelling complex phenomena across fields such as neuroscience, condensed matter, and high-energy physics. However, identifying higher-order topological structures -- such as $k$-cliques, fundamental building blocks of complex networks -- remains a significant challenge. Here we develop a universal programmable photonic quantum processor that enables the encoding of arbitrary complex-weight networks, providing a direct pathway to uncovering their topological structures. We demonstrate how this quantum approach can identify weighted $k$-cliques and estimate Betti numbers by leveraging the Gaussian boson sampling algorithm's ability to preferentially select high-weight, dense subgraphs. The unique capabilities of our programmable quantum processor allow us to observe topological phase transitions and identify clique percolation phenomena directly from the entropy of the sampling results. These findings showcase how photonic quantum computing can be applied to analyse the topological characteristics of real-world complex networks, opening new possibilities for quantum-enhanced data analysis.
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Submitted 14 July, 2025; v1 submitted 10 July, 2025;
originally announced July 2025.
Exchange-Symmetrized Qudit Bell Bases and Bell-State Distinguishability
Authors:
Oscar Scholin,
Theresa W. Lynn
Abstract:
Entanglement of qudit pairs, with single particle Hilbert space dimension $d$, has important potential for quantum information processing, with applications in cryptography, algorithms, and error correction. For a pair of qudits of arbitrary even dimension $d$, we introduce a generalized Bell basis with definite symmetry under exchange of internal states between the two particles. We show that no…
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Entanglement of qudit pairs, with single particle Hilbert space dimension $d$, has important potential for quantum information processing, with applications in cryptography, algorithms, and error correction. For a pair of qudits of arbitrary even dimension $d$, we introduce a generalized Bell basis with definite symmetry under exchange of internal states between the two particles. We show that no complete exchange-symmetrized basis can exist for odd $d$. This framework extends prior work on exchange-symmetrized hyperentangled qubit bases, where $d$ is a power of two. For our exchange-symmetrized basis we show that measurement devices restricted to linear evolution and local measurement (LELM) can unambiguously distinguish $2d-1$ qudit Bell states for any even $d$. This achieves the upper bound in general for reliable Bell-state distinguishability via LELM and augments previously known limits for $d = 2^n$ and $d=3$. This result is relevant to near-term realizations of quantum communication protocols.
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Submitted 20 May, 2025; v1 submitted 13 December, 2024;
originally announced December 2024.