{"paper":{"title":"Quantum Simulation of Differential-Algebraic Equations with Applications to Unsteady Stokes Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A dilation framework embeds non-Hermitian DAE dynamics into projected Schrödinger evolution for quantum simulation.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Hsuan-Cheng Wu, Xiantao Li","submitted_at":"2026-05-01T17:21:52Z","abstract_excerpt":"Differential-algebraic equations (DAEs) arise naturally in constrained dynamical systems, but their algebraic constraints and hidden compatibility conditions make them more subtle than standard ordinary differential equations. This paper initiates a quantum-algorithmic study of constrained linear DAEs. We introduce a dilation framework that embeds the generally non-Hermitian constrained evolution into a projected Schr\\\"odinger-type dynamics on an enlarged Hilbert space, \\[ i\\frac{d}{dt}\\Psi(t)=P\\widehat H P\\Psi(t), \\] where $\\widehat H$ is Hermitian and $P$ is the orthogonal projector onto the"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce a dilation framework that embeds the generally non-Hermitian constrained evolution into a projected Schrödinger-type dynamics on an enlarged Hilbert space, i d/dt Ψ(t) = P H P Ψ(t), where H is Hermitian and P is the orthogonal projector onto the lifted constraint subspace. This identifies the DAE evolution with a quantum Zeno-type dynamics and enables the use of block encodings, QSVT-based projector construction, and Hamiltonian simulation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the orthogonal projector P onto the lifted constraint subspace can be efficiently constructed via QSVT and that low-energy spectral cutoffs motivated by solution smoothness remain valid without introducing prohibitive approximation errors in the Stokes application.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new dilation embeds non-Hermitian DAE evolution into projected Hermitian quantum dynamics, enabling block encodings and QSVT for simulation of constrained systems like unsteady Stokes flow.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A dilation framework embeds non-Hermitian DAE dynamics into projected Schrödinger evolution for quantum simulation.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"33bdc94aaee19c1d9b83b425883bb6b5f22a4aa1394959583a4869626074f52f"},"source":{"id":"2605.00794","kind":"arxiv","version":2},"verdict":{"id":"2ab0cc72-dcbc-4763-ac29-78e75f5e9084","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T19:20:05.224676Z","strongest_claim":"We introduce a dilation framework that embeds the generally non-Hermitian constrained evolution into a projected Schrödinger-type dynamics on an enlarged Hilbert space, i d/dt Ψ(t) = P H P Ψ(t), where H is Hermitian and P is the orthogonal projector onto the lifted constraint subspace. This identifies the DAE evolution with a quantum Zeno-type dynamics and enables the use of block encodings, QSVT-based projector construction, and Hamiltonian simulation.","one_line_summary":"A new dilation embeds non-Hermitian DAE evolution into projected Hermitian quantum dynamics, enabling block encodings and QSVT for simulation of constrained systems like unsteady Stokes flow.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the orthogonal projector P onto the lifted constraint subspace can be efficiently constructed via QSVT and that low-energy spectral cutoffs motivated by solution smoothness remain valid without introducing prohibitive approximation errors in the Stokes application.","pith_extraction_headline":"A dilation framework embeds non-Hermitian DAE dynamics into projected Schrödinger evolution for quantum simulation."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.00794/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T17:49:38.678165Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"dd451f3122d816fb745871668b34e775ce8f0994659a38b2bb4a523f549f6ca4"},"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"}