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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. 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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","authors_text":"Abeynaya Gnanasekaran, Amit Surana, Daniel Gunlycke, Reuben Demirdjian, Thomas Hogancamp","cross_cats":[],"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.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-05-01T00:10:50Z","title":"Quantum Data Loading for Carleman Linearized Systems: Application to the Lattice-Boltzmann Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.00302","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-12T05:18:41.352492Z","id":"bf4f3dee-2d82-428c-a591-b9913a629850","model_set":{"reader":"grok-4.3"},"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","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.","strongest_claim":"we construct a generalized LCU framework for any Carleman linearized autonomous dynamical system with a polynomial nonlinearity. 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