{"paper":{"title":"A combinatorial framework for clustering graph states: Algorithms and hardness for rank-integrity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","quant-ph"],"primary_cat":"cs.DS","authors_text":"Blair D. Sullivan, Nathan Claudet, Romain Bourneuf, Rose McCarty, Sang Yoon Kim, St\\'ephan Thomass\\'e","submitted_at":"2026-07-10T14:42:55Z","abstract_excerpt":"We introduce a new notion of distance between two graph states $|G\\rangle$ and $|G'\\rangle$ on the same set of qubits. This distance is the minimum number of ancilla qubits in a graph state $|\\widehat{G}\\rangle$ from which both $|G\\rangle$ and $|G'\\rangle$ can be ``easily prepared''. (When preparing graph states, we are only allowed to use one-qubit Clifford gates, one-qubit Pauli measurements, and classical communication.) We give a graphical description of this distance through the lens of vertex-minors. We then show how this distance yields quantum network analogs of many graph edit-distanc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09469","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.09469/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}