Quantum embedding of graphs for subgraph counting
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913048958074880 |
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| author | Adhikari, Bibhas |
| author_facet | Adhikari, Bibhas |
| contents | We develop a unified quantum framework for subgraph counting in graphs. We encode a graph on $N$ vertices into a quantum state on $2\lceil \log_2 N \rceil$ working qubits and $2$ ancilla qubits using its adjacency list, with worst-case gate complexity $O(N^2)$, which we refer to as the graph adjacency state. We design quantum measurement operators that capture the edge structure of a target subgraph, enabling estimation of its count via measurements on the $m$-fold tensor product of the adjacency state, where $m$ is the number of edges in the subgraph. We illustrate the framework for triangles, cycles, and cliques. This approach yields quantum logspace algorithms for motif counting, with no known classical counterpart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18754 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum embedding of graphs for subgraph counting Adhikari, Bibhas Quantum Physics Computational Complexity We develop a unified quantum framework for subgraph counting in graphs. We encode a graph on $N$ vertices into a quantum state on $2\lceil \log_2 N \rceil$ working qubits and $2$ ancilla qubits using its adjacency list, with worst-case gate complexity $O(N^2)$, which we refer to as the graph adjacency state. We design quantum measurement operators that capture the edge structure of a target subgraph, enabling estimation of its count via measurements on the $m$-fold tensor product of the adjacency state, where $m$ is the number of edges in the subgraph. We illustrate the framework for triangles, cycles, and cliques. This approach yields quantum logspace algorithms for motif counting, with no known classical counterpart. |
| title | Quantum embedding of graphs for subgraph counting |
| topic | Quantum Physics Computational Complexity |
| url | https://arxiv.org/abs/2604.18754 |