{"paper":{"title":"Quantum Data Loading for Carleman Linearized Systems: Application to the Lattice-Boltzmann Equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A decomposition of any square matrix into non-unitaries yields an LCU for Carleman-linearized systems whose term count depends only on truncation order and velocity count.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Abeynaya Gnanasekaran, Amit Surana, Daniel Gunlycke, Reuben Demirdjian, Thomas Hogancamp","submitted_at":"2026-05-01T00:10:50Z","abstract_excerpt":"Herein, we introduce a strategy to decompose an arbitrary square matrix into a linear combination of non-unitaries (LCNU) where each non-unitary term is embedded into a unitary matrix. The result is a linear combination of unitaries (LCU) with an equal number of terms as the LCNU. Using this approach, we construct a generalized LCU framework for any Carleman linearized autonomous dynamical system with a polynomial nonlinearity. This framework is then used to construct an LCU for the 3-dimensional Carleman linearized lattice Boltzmann equation (LBE) in which the number of terms scales like $N_s"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we construct a generalized LCU framework for any Carleman linearized autonomous dynamical system with a polynomial nonlinearity. This framework is then used to construct an LCU for the 3-dimensional Carleman linearized lattice Boltzmann equation (LBE) in which the number of terms scales like Ns ∼ O(α² Q²), where α is the Carleman truncation order and Q is the number of discrete velocities from the LBE. Importantly, Ns is completely independent of both the number of temporal and spatial discretization points.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That an arbitrary square matrix representing the Carleman-linearized system can be decomposed into a linear combination of non-unitaries whose count scales as O(α² Q²) and that each non-unitary can be embedded into a unitary without introducing discretization-dependent overheads that would invalidate the claimed independence.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new LCNU-to-LCU decomposition enables a generalized quantum framework for Carleman-linearized polynomial systems like the lattice Boltzmann equation, with Ns scaling as O(α² Q²) independent of spatial and temporal discretization points.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A decomposition of any square matrix into non-unitaries yields an LCU for Carleman-linearized systems whose term count depends only on truncation order and velocity count.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3b433e5aff4a0027a1eb53e4a9816c989cd1d9e8fd9e8d39879c54eac8763681"},"source":{"id":"2605.00302","kind":"arxiv","version":3},"verdict":{"id":"bf4f3dee-2d82-428c-a591-b9913a629850","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T05:18:41.352492Z","strongest_claim":"we construct a generalized LCU framework for any Carleman linearized autonomous dynamical system with a polynomial nonlinearity. This framework is then used to construct an LCU for the 3-dimensional Carleman linearized lattice Boltzmann equation (LBE) in which the number of terms scales like Ns ∼ O(α² Q²), where α is the Carleman truncation order and Q is the number of discrete velocities from the LBE. Importantly, Ns is completely independent of both the number of temporal and spatial discretization points.","one_line_summary":"A new LCNU-to-LCU decomposition enables a generalized quantum framework for Carleman-linearized polynomial systems like the lattice Boltzmann equation, with Ns scaling as O(α² Q²) independent of spatial and temporal discretization points.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That an arbitrary square matrix representing the Carleman-linearized system can be decomposed into a linear combination of non-unitaries whose count scales as O(α² Q²) and that each non-unitary can be embedded into a unitary without introducing discretization-dependent overheads that would invalidate the claimed independence.","pith_extraction_headline":"A decomposition of any square matrix into non-unitaries yields an LCU for Carleman-linearized systems whose term count depends only on truncation order and velocity count."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.00302/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T18:16:34.021837Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1cbed07eb4ff4f5edb1b1fc7242a1bb11372d5d917427e194584cbb9ea47509f"},"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"}