{"paper":{"title":"Universality of Photonic Interlacing Architectures for Learning Discrete Linear Unitaries","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.MP","physics.optics"],"primary_cat":"quant-ph","authors_text":"Alexey Ovchinnikov, Kevin Zelaya, Matthew Markowitz, Mohammad-Ali Miri","submitted_at":"2025-06-10T05:18:47Z","abstract_excerpt":"Recent investigations suggest that the discrete linear unitary group $U(N)$ can be represented by interlacing a finite sequence of diagonal phase operations with an intervening unitary operator. However, despite rigorous numerical justifications, no formal proof has been provided. Here, we show that elements of $U(N)$ can be decomposed into a sequence of $N$-parameter phases alternating with $1$-parameter propagators of a lattice Hamiltonian. The proof is based on building a Lie group by alternating these two operators and showing its completeness to represent $U(N)$ for a finite number of lay"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08454","kind":"arxiv","version":2},"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/2506.08454/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"}