Boundary-Aware QFT Block-Encoding of Fractional Laplacians
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Quantum Physics arXiv:2605.16749 (quant-ph) [Submitted on 16 May 2026] Title:Boundary-Aware QFT Block-Encoding of Fractional Laplacians Authors:Younes Javanmard, Sina Kazemian View a PDF of the paper titled Boundary-Aware QFT Block-Encoding of Fractional Laplacians, by Younes Javanmard and Sina Kazemian View PDF HTML (experimental) Abstract: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. We identify this mismatch through an exact Toeplitz-to-circulant aliasing identity. To recover the open-boundary action, we zero-pad the state into a larger \(M\)-point QFT register, apply the same Fourier-symbol block-encoding, and compress back to the physical subspace. The resulting compressed block satisfies \(P_{N\to M}^{\dagger}\widetilde A^{(M)}_{\alpha,h}P_{N\to M} = A^{(N)}_{\alpha,h}+E^{(M)}\), where \(E^{(M)}\) is controlled by the tail of the semi-discrete convolution kernel. Thus, the QFT layer implements the fractional symbol, while zero-padding supplies the open-boundary geometry. The construction is an operator-compilation primitive for boundary-aware quantum simulation rather than a complete PDE solver. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.16749 [quant-ph] (or arXiv:2605.16749v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.16749 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Sina Kazemian [view email] [v1] Sat, 16 May 2026 02:06:47 UTC (361 KB) Full-text links: Access Paper: View a PDF of the paper titled Boundary-Aware QFT Block-Encoding of Fractional Laplacians, by Younes Javanmard and Sina KazemianView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)