QuIC: A Training-Free Quantum Graph Embedding from Ideal Analysis to Practical Hardware Evaluation

Quantum Physics [Submitted on 20 Apr 2026] QuIC: A Training-Free Quantum Graph Embedding from Ideal Analysis to Practical Hardware Evaluation Luke Miller, Yugyung Lee We introduce QuIC, a training-free quantum graph embedding that maps graphs to sorted output distributions via a fixed parameterized circuit. In the ideal one-repetition setting, we prove that the resulting sorted distribution is permutation-invariant and injective on labeled graphs under an irrational-angle condition, yielding completeness on isomorphism classes for the ideal one-repetition exact-arithmetic embedding. We then use those ideal structural properties to motivate a practical embedding pipeline and study how much of that behavior survives under finite-shot estimation, truncation, realistic noise, transpilation, and hardware execution. The sorted distribution concentrates discriminative signal in a compact head, making fixed-length head truncation an effective practical operating point in the tested regimes. Under noise-model simulation, all tested graph pairs satisfied the study's operational separation criterion, including strongly regular graph pairs that are standard 2-WL stress tests and CFI families used as hard instances for fixed-k WL methods. A hardware study comprising 14,800 transpiled circuits across 37 CFI families on IBM Heron (ibm_fez, 156 qubits), including paired one- and two-repetition evaluations, reports empirical separation up to 66 qubits for the tested families under the reported execution protocol, identifies a device-dependent depth limit near 210-250 layers, and characterizes the current practical boundary of the method under the reported execution protocol. Comments: 18 pages, 6 figures, 9 tables Subjects: Quantum Physics (quant-ph) MSC classes: 81P68, 05C60, 68Q17 ACM classes: F.1.2; F.2.2; G.4; I.2.8 Cite as: arXiv:2604.18841 [quant-ph]   (or arXiv:2604.18841v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.18841 Focus to learn more Submission history From: Yugyung Lee [view email] [v1] Mon, 20 Apr 2026 21:09:12 UTC (359 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 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?)