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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.16749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-16T02:06:47Z","cross_cats_sorted":[],"title_canon_sha256":"534f247259bee13164317d67d71e494f19fd7e7992a5e918c510721601d3c269","abstract_canon_sha256":"529534859ffee6cf071dce8a1ba7a522aaa95a252ca6396fb4dc2826c18a1799"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:19.597625Z","signature_b64":"Pthj3mLl5IvOXN4a8Ea5k5waUBRR65ayvxL2WfjCxAJ9zuRred39soL/wiVf5IyrRoxqgGkWcT1piMHKfCoGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e57f1f817ca4a3083036ff0a3354342c4bd468ee73b7920397e6c9cbeb9f1347","last_reissued_at":"2026-05-20T00:03:19.596548Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:19.596548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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