{"paper":{"title":"Shallow Unitary Circuits for Kramers-Wannier Dualities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.quant-gas","cond-mat.str-el"],"primary_cat":"quant-ph","authors_text":"Shang Liu, Yanting Cheng","submitted_at":"2026-07-02T02:44:27Z","abstract_excerpt":"The quantum Kramers-Wannier (KW) duality is a fundamental transformation mapping short-range entangled (SRE) states to long-range entangled (LRE) states. While spatially local unitary circuits require linear-in-system-size depth to implement this duality, the ultimate speed limit for purely unitary circuits equipped with nonlocal connectivity remains an open question. Here, we explicitly construct logarithmic depth, spatially nonlocal unitary circuits that realize the exact $\\mathbb{Z}_2$ KW dualities in both one and two spatial dimensions. We further generalize the construction to arbitrary $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01624","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/2607.01624/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"}