QuIC: A Training-Free Quantum Graph Embedding from Ideal Analysis to Practical Hardware Evaluation
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| Format: | Preprint |
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2026
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| _version_ | 1866911610785759232 |
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| author | Miller, Luke Lee, Yugyung |
| author_facet | Miller, Luke Lee, Yugyung |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_18841 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | QuIC: A Training-Free Quantum Graph Embedding from Ideal Analysis to Practical Hardware Evaluation Miller, Luke Lee, Yugyung Quantum Physics 81P68, 05C60, 68Q17 F.1.2; F.2.2; G.4; I.2.8 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. |
| title | QuIC: A Training-Free Quantum Graph Embedding from Ideal Analysis to Practical Hardware Evaluation |
| topic | Quantum Physics 81P68, 05C60, 68Q17 F.1.2; F.2.2; G.4; I.2.8 |
| url | https://arxiv.org/abs/2604.18841 |