Metraipolis › archive › dc_4022ea5eabc5

Completeness for flow-preserving rewrite rules — arXiv:2608.13035

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.13035
License (as archived): CC0-1.0
Archived: 2026-10-19T05:05:04.112Z
SHA-256 of the archived text: 5f3c166f97357f8540eb0710a415ed2c5c44c12cd4bea68a6cd550ad4c1fdb6e
Stable URL of this page: https://metraipolis.com/documento/dc_4022ea5eabc5

How to cite

Completeness for flow-preserving rewrite rules — arXiv:2608.13035 — arXiv (en), https://arxiv.org/abs/2608.13035 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_4022ea5eabc5 (Metraipolis archive dc_4022ea5eabc5, sha256 5f3c166f97357f8540eb0710a415ed2c5c44c12cd4bea68a6cd550ad4c1fdb6e)

BibTeX

@misc{dc4022ea5eabc5,
  title = {Completeness for flow-preserving rewrite rules — arXiv:2608.13035},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.13035},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_4022ea5eabc5; sha256 5f3c166f97357f8540eb0710a415ed2c5c44c12cd4bea68a6cd550ad4c1fdb6e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.13035. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Complete sets of graphical rewrite rules enable fully graphical reasoning about quantum computations and have been an area of active research for more than a decade. Many recent applications of the ZX-calculus have made use of the close correspondence between ZX-diagrams and computations in the one-way model of measurement-based quantum computation. In this model, various kinds of flow properties ensure deterministic implementability; for ZX-diagrams, these same properties allow efficient translation into quantum circuits (a problem that is known to be #P-hard in general). Therefore, flow-preserving ZX-calculus rewrite rules are of strong interest. Here, we extend the set of flow-preserving rules appearing in the literature with a few new rules and extensions of existing rules. We then show that the resulting rule set is complete for all flow-preserving translations between ZX-diagrams of appropriate form. The proof employs a manifestly flow-preserving equivalent of circuit extraction, where a diagram with gflow is transformed, using only flow-preserving rewrite rules, into a diagram with causal flow.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-08-14 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2608.13035 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T04:54:42.507Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-08-14?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).