Quantum embedding of graphs for subgraph counting

Quantum Physics [Submitted on 20 Apr 2026] Quantum embedding of graphs for subgraph counting Bibhas Adhikari 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. Subjects: Quantum Physics (quant-ph); Computational Complexity (cs.CC) Cite as: arXiv:2604.18754 [quant-ph]   (or arXiv:2604.18754v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.18754 Focus to learn more Submission history From: Bibhas Adhikari [view email] [v1] Mon, 20 Apr 2026 18:58:35 UTC (599 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.CC References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)