{"paper":{"title":"Enabling Lie-Algebraic Classical Simulation beyond Free Fermions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Symmetry-adapted bases enable polynomial-cost Lie-algebraic simulation beyond free fermions.","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Adelina B\\\"arligea, Jakob S. Kottmann, Matthew L. Sims-Goh","submitted_at":"2026-04-17T21:05:34Z","abstract_excerpt":"Efficient classical simulation has matured to a critical component of the quantum computing stack, driving hardware validation, algorithm design, benchmarking, and the study of structured quantum dynamics. Lie-algebraic simulation ($\\mathfrak{g}$-sim) offers a compelling approach: it represents Heisenberg-picture dynamics in the adjoint space whose dimension is set by the dynamical Lie algebra (DLA) governing the circuit, enabling efficient simulation of expectation values whenever the DLA grows only polynomially with system size. Despite this promise, existing applications of $\\mathfrak{g}$-s"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we develop an explicit Pauli orbit basis for permutation-equivariant dynamics, supporting cubic-dimensional algebras despite exponential Pauli support, and a subspace-adapted (modified) generalized Gell-Mann basis for bounded Hamming-weight (U(1)-equivariant) dynamics, yielding polynomial costs on fixed excitation sectors.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the newly identified dynamical Lie algebras remain polynomially bounded in dimension and that the symmetry-adapted bases render the adjoint-space mapping computationally tractable for the targeted circuit families.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"New Pauli orbit and modified Gell-Mann bases enable polynomial-cost Lie-algebraic simulation for permutation-equivariant and bounded-excitation quantum dynamics.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Symmetry-adapted bases enable polynomial-cost Lie-algebraic simulation beyond free fermions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"bc6adda5e78eb630b0fcf3698cdb36cb6f6159b347607371c3889942a5ad6652"},"source":{"id":"2604.16701","kind":"arxiv","version":2},"verdict":{"id":"12eb3bd2-a6ac-40b6-a976-ed698b542234","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T07:56:40.021869Z","strongest_claim":"we develop an explicit Pauli orbit basis for permutation-equivariant dynamics, supporting cubic-dimensional algebras despite exponential Pauli support, and a subspace-adapted (modified) generalized Gell-Mann basis for bounded Hamming-weight (U(1)-equivariant) dynamics, yielding polynomial costs on fixed excitation sectors.","one_line_summary":"New Pauli orbit and modified Gell-Mann bases enable polynomial-cost Lie-algebraic simulation for permutation-equivariant and bounded-excitation quantum dynamics.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the newly identified dynamical Lie algebras remain polynomially bounded in dimension and that the symmetry-adapted bases render the adjoint-space mapping computationally tractable for the targeted circuit families.","pith_extraction_headline":"Symmetry-adapted bases enable polynomial-cost Lie-algebraic simulation beyond free fermions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.16701/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"}