{"paper":{"title":"Boundary-Aware QFT Block-Encoding of Fractional Laplacians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Zero-padding a state into a larger QFT register recovers the open-boundary fractional Laplacian from a circulant encoding up to a kernel-tail error.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Sina Kazemian, Younes Javanmard","submitted_at":"2026-05-16T02:06:47Z","abstract_excerpt":"We study the quantum Fourier transform (QFT) block-encoding of the semi-discrete fractional Laplacian on bounded domains with open, zero-extension boundary conditions. In the notation of the main construction, the target operator is the finite Toeplitz truncation \\(A^{(N)}_{\\alpha,h}\\) obtained from the full-lattice semi-discrete operator with symbol \\(|\\xi|^\\alpha\\). A finite QFT register, however, diagonalizes circulant matrices rather than Toeplitz truncations. The native QFT circuit therefore implements a periodic surrogate \\(\\widetilde A^{(N)}_{\\alpha,h}\\), not the open-boundary operator."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The resulting compressed block satisfies P_{N→M}^† Ã^{(M)}_{α,h} P_{N→M} = A^{(N)}_{α,h} + E^{(M)}, where E^{(M)} is controlled by the tail of the semi-discrete convolution kernel.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That zero-padding into an M-point register followed by compression recovers the open-boundary Toeplitz action up to an error term whose size is governed solely by the kernel tail (abstract, section on the aliasing identity).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The paper presents a zero-padding method to make QFT block-encodings match open-boundary Toeplitz truncations of fractional Laplacians instead of periodic circulant surrogates.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Zero-padding a state into a larger QFT register recovers the open-boundary fractional Laplacian from a circulant encoding up to a kernel-tail error.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f45a68833615863955bb118482bf63e911c1fddb2fe8c3068c73790b4a3d895e"},"source":{"id":"2605.16749","kind":"arxiv","version":1},"verdict":{"id":"a56e96fb-3db5-4851-b5ba-e7424e7c1ee9","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T21:18:52.527785Z","strongest_claim":"The resulting compressed block satisfies P_{N→M}^† Ã^{(M)}_{α,h} P_{N→M} = A^{(N)}_{α,h} + E^{(M)}, where E^{(M)} is controlled by the tail of the semi-discrete convolution kernel.","one_line_summary":"The paper presents a zero-padding method to make QFT block-encodings match open-boundary Toeplitz truncations of fractional Laplacians instead of periodic circulant surrogates.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That zero-padding into an M-point register followed by compression recovers the open-boundary Toeplitz action up to an error term whose size is governed solely by the kernel tail (abstract, section on the aliasing identity).","pith_extraction_headline":"Zero-padding a state into a larger QFT register recovers the open-boundary fractional Laplacian from a circulant encoding up to a kernel-tail error."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16749/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T21:31:19.377530Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T21:31:13.995659Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.328040Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.458544Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"375ec02402ba55e6e928a478176b05e7d70faf3b69e2251d2b7d8539d630c267"},"references":{"count":42,"sample":[{"doi":"","year":2000,"title":"R. 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