{"paper":{"title":"Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Qudit encodings can cut non-Clifford costs by constant factors over qubits for diagonal quadratic operators at small d in LCU settings, but qubits scale better asymptotically and dominate product formulas.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alessandro Roggero, Do\\u{g}a Murat K\\\"urk\\c{c}\\\"uo\\u{g}lu, Gabriel N. Perdue, Marina Maneyro, Samuel Godwood","submitted_at":"2026-04-29T15:25:08Z","abstract_excerpt":"Finite local Hilbert-space truncations arise naturally in quantum simulations of lattice field theories and motivate qudit encodings, but their fault-tolerant advantage over qubit encodings remains unclear. We compare the non-Clifford cost of implementing quadratic diagonal evolutions, exemplified by $U=e^{-it\\phi_x^2}$ in a uniform field-amplitude discretization of a real scalar field, using either one logical $d$-level qudit or $n_b=\\lceil \\log_2 d\\rceil$ logical qubits. We analyze two standard settings: product-formula simulation and LCU/block encoding, taking the resource metric to be the "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Within the constructive models studied here, product-formula implementations would require an exponentially stronger per-primitive synthesis advantage for qudits to win asymptotically, while in the LCU setting the qubit encoding is asymptotically cheaper in d. Nevertheless, the finite-d threshold analysis identifies low dimensional regions in which qudits can yield meaningful constant-factor savings, particularly for LCU-based implementations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Because tight synthesis bounds for general single-qudit rotations are not known, we express the qudit constructions in terms of embedded two-level SU(2) rotations; this modeling choice and the idealized negligible-overhead qubit-qudit code-switching model are load-bearing for the break-even conditions and T-count comparisons.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Qudit encodings for quadratic diagonal evolutions require exponentially stronger synthesis advantages than qubits to win asymptotically in product formulas but can yield constant-factor savings in LCU at low d.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Qudit encodings can cut non-Clifford costs by constant factors over qubits for diagonal quadratic operators at small d in LCU settings, but qubits scale better asymptotically and dominate product formulas.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b1ff8257426a046ffe41476da38fb4a1dd834a8265c3e1910639d21aa9126708"},"source":{"id":"2604.26792","kind":"arxiv","version":2},"verdict":{"id":"94c2b9b1-6bd4-4f6a-87e9-3d05052b0332","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T13:10:14.911795Z","strongest_claim":"Within the constructive models studied here, product-formula implementations would require an exponentially stronger per-primitive synthesis advantage for qudits to win asymptotically, while in the LCU setting the qubit encoding is asymptotically cheaper in d. Nevertheless, the finite-d threshold analysis identifies low dimensional regions in which qudits can yield meaningful constant-factor savings, particularly for LCU-based implementations.","one_line_summary":"Qudit encodings for quadratic diagonal evolutions require exponentially stronger synthesis advantages than qubits to win asymptotically in product formulas but can yield constant-factor savings in LCU at low d.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Because tight synthesis bounds for general single-qudit rotations are not known, we express the qudit constructions in terms of embedded two-level SU(2) rotations; this modeling choice and the idealized negligible-overhead qubit-qudit code-switching model are load-bearing for the break-even conditions and T-count comparisons.","pith_extraction_headline":"Qudit encodings can cut non-Clifford costs by constant factors over qubits for diagonal quadratic operators at small d in LCU settings, but qubits scale better asymptotically and dominate product formulas."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26792/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T23:41:45.090461Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:46:05.247669Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ef433e25d6b8a13751c0e865de0d4b835e01fb70b73f6ed99ed8b6cded1d1e78"},"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"}